Liverpool laid to rest any fears the Premier League title race pressure would get too much with a breathless start against Norwich on Sunday.
The Reds took the lead after just four minutes at Carrow Road, with fluid build-up play between Joe Allen, Jon Flanagan and Philippe Coutinho teeing up Raheem Sterling 35 yards from goal.
The youngster let fly with a sensational shot that took a slight touch of Michael Turner's back and flew past John Ruddy, giving the Norwich goalkeeper no chance of making a save whatsoever.
The travelling fans were already singing "Now you're gonna believe us, we're going to win the league" when Steven Gerrard sent Sterling galloping down the left to carve out a good cross that Suarez finishes from close range - his 30th Premier League goal of the season.
The hosts showed plenty of signs that they were not out of the game yet, but with their players becoming increasingly frustrated Robert Snodgrass made a nasty challenge on Joe Allen and became the first player to be booked.
Despite the increasing pressure from the home side, Brendan Rodgers' side stood firm.
Redmond threatened to change that when breaking into the box on the right hand side but his shot was wild when teammates were better placed in the centre, and then Gary Hooper was denied an opportunity when Simon Mignolet rushed out to claim a ball that was bobbling around the six-yard box.
Norwich came back quickly in the second half, Gary Hooper taking advantage of an unconvincing clearance from Mignolet to tap the ball home from just yards into an open goal, halving the deficit.
But the celebrations didn't last long as Raheem Sterling proved his worth once again. Intercepting a sloppy pass from Bradley Johnson and running the entire length of the Norwich half, he got past a couple of defenders to shoot on target. His attempt deflected off Johnson's legs and over a helpless John Ruddy.
Neil Adams' side were fighting for their lives, trying again and again to get another goal in the net.
And it was Robert Snodgrass who got the hosts back in the game, directing a fine header into the top right-hand corner of Mignolet's net to make it 2-3.
Hungry for an equaliser, Norwich sent on two attackers Josh Murphy and Ricky van Wolfswinkel.
The Dutch striker nearly did it, firing a downward header straight at Mignolet and creating an extremely nervous spell for Liverpool.
Brendan Rodgers' men struggled to keep hold of the ball as four minutes of stoppage time went on the board.
And with seconds remaining Norwich won a free-kick just inside the Liverpool half. Even goalkeeper John Ruddy ran to the opposite end of the pitch to join every Canaries player - but Liverpool held firm at the death and go five points clear at the top of the table.
Ruddy, Whittaker, Martin, Turner, Olsson, Johnson, Howson, Fer, Snodgrass, Redmond, Hooper
Subs: Bunn, Van Wolfswinkel, Gutierrez, Garrido, R. Bennett, Tettey, Josh Murphy
Mignolet, Johnson, Skrtel, Sakho, Flanagan, Gerrard, Lucas, Allen, Sterling, Coutinho, Suarez
Subs: Jones, Toure, Agger, Cissokho, Moses, Alberto, Aspas
Rodgers: Sterling is best young player in Europe
Liverpool manager Brendan Rodgers hailed the performance of teenager Sterling in the win which keeps the title race firmly in his side's hands.
"He is the best young player in European football at the moment," Rodgers said.
"At 19 years of age you don't see anyone better. His intelligence with the ball, his movement and he's scoring goals. His first goal was a wonderful strike. He's just shifted it, got his shot off; to beat a goalkeeper of John Ruddy's quality shows you the quality of the strike.
"His pass for Luis' goal was like a top midfield player, so there's an assist, and his position for the counter attack when he broke away and obviously gets a bit of luck on the deflection but his overall performance he's shown so much maturity."
The Northern Irishman also revealed how he inspired his side ahead of kick-off following an emotional week for the club.
He said: "We've come off the back of the week where we held the memorial service for Hillsborough. We used Margaret Aspinall (chair of the Hillsborough Family Support Group), one of her quotes she made on the day as a real motivation for us going into the game and real encouragement for us and the players are helping themselves.
"They're winning games and they are very hungry. We have qualified for the Champions League. That was the objective and we can finish no lower than third which is an incredible achievement for the team and the squad."
Qualification for the Champions League and winning the Premier League title are within Liverpool's grasp, and the Reds boss also said they want to hit another target.
He said: "We have a performance goal. We want to reach 100 plus goals and we're now on 96. There are only three teams in the history of the Premier League that have got 100 goals or more. We want to try and push for that in the final three games."
Suarez: My only focus is title glory
Liverpool striker Luis Suarez scored his 30th goal of the season for the Reds in Easter Sunday's 3-2 win over relegation-threatened Norwich at Carrow Road but said his only focus is on title glory.
Raheem Sterling scored twice and Suarez was also on target as the Merseyside club moved five points clear of second-placed Chelsea at the top of the Barclays Premier League table.
Liverpool romped to a 2-0 lead inside 10 minutes as the Canaries were ripped apart with a superb 25-yard effort from Sterling, before Suarez tucked home from close range.
However, Norwich - just two points above the drop zone - rallied after Gary Hooper reduced the deficit following a poor punch by Simon Mignolet only for Sterling to slot home a deflected third on the break.
Robert Snodgrass set up a tense finale with his header with 13 minutes left, but the Reds secured what looks to be a priceless victory in their bid to win a first championship in more than 20 years.
After the match, Suarez, who became the first Liverpool player to score 30 goals in one season since Ian Rush achieved the feat in 1987, told Sky Sports News: "Of course we are happy because those three points are important for us and we worked really hard today against Norwich.
"Every time they are difficult (to play) and they are fighting not to go down and we know that.
"(The 30 goals) is important for myself but my target is to help the team every time. We are on the top now and we enjoy that."
However, with Jose Mourinho's Chelsea up next at Anfield, the Uruguay international is not popping the champagne corks to celebrate just yet.
He added: "In football you never know what will happen. We will keep calm and focus on the next game against Chelsea."
Adams: Liverpool punished us
Norwich manager Neil Adams knows his side face a tough task to stave off relegation with games against Manchester United, Chelsea and Arsenal making up their remaining fixtures.
However, he was able to find positives in the defeat by Liverpool which he hopes to carry into those games.
Adams said: "I thought we deserved something from the game, particularly with the second-half performance. The first-half performance wasn't good enough. We were playing against a top team and you can't give these types of team an inch or they will punish you.
"They are at the top of the table and that's why they've got top-class players in their side and we didn't get close enough in the tackles. We were a little bit shy with our passing and maybe a bit off the pace. Certainly in the second half I couldn't ask any more of them.
"The application from the players (in the second half) was precisely the response that you want. What you don't want is Liverpool running all over you and dominating the game and from the first whistle in the second half you could see we were about it.
"We had that belief we could go on and do something against a top side and the key message from that is that we've got three key games coming up. The second half performance is what we need in those three (games) and if we can do that we're still very confident we can get enough points to stay in the division."
Steven Gerrard hails 'phenomenal' Brendan Rodgers
Liverpool captain Steven Gerrard has hailed manager Brendan Rodgers as "phenomenal" and hopes the Northern Irishman can build a legacy at the club.
The pair have been at the forefront of Liverpool's Barclays Premier League title charge, which was strengthened by rivals Manchester City and Chelsea both slipping up against Sunderland this week.
A top-four finish was the stated aim this season for the Reds, who have finished no higher than sixth in the past four campaigns, but they have thrived under Rodgers
Gerrard told the Daily Telegraph: "He's a phenomenal man for his age (41). I think he's going to grow into one of the world's best managers and I hope he is here long after I am gone.
"I hope he is here for many, many years because this club is in great hands. Whatever happens now until the end of the season, it's safe.
"He's a winner, he's hungry for success, he does the right things, he treats players well, he doesn't try and control the football club, or get involved in stuff that has nothing to do with him.
"He just focuses on getting on the training pitch and coaching the team, improving individuals, improving the team and playing football the right way. That's what the supporters want here."
The Merseysiders currently top the standings by five points, after today's clash with Norwich, and are now firm favourites to earn their first league success in 24 years, with captain Gerrard admitting he will need to keep his emotions in check during the run-in.
"They are there - the nerves, the excitement. They are there because we have earned the right to have those kinds of feelings," he added.
"The challenge for me, which just as important as being on the pitch now, is can I control myself and can I get on with my life for the next four weeks."
The impact of Gerrard
Liverpool captain Steven Gerrard lead his side to a 3-2 victory in Sunday's Barclays Premier League game against Norwich.
Here, Jim van Wijk examines the impact of the England midfielder at Carrow Road.
Gerrard was out early to join the warm-up, quick to salute the massed ranks of travelling Reds supporters packed into the far corner of the Jarrold Stand - many of whom will have left Merseyside in the early hours of Easter Sunday to make the long journey across to Norfolk.
The Liverpool skipper did not have to wait long to lead the celebrations after Raheem Sterling's superb opening goal on four minutes set them on the way. He remained calm as Liverpool's character was tested to help guide his side through following a Norwich fight-back in the second half.
He was happy to sit back when needed to help block what little attacking threat Norwich were able to muster, dropping deep to protect Martin Skrtel and Mamadou Sakho, before then collecting the ball and starting another probing Liverpool move via Lucas and Joe Allen.
Gerrard also provided good delivery from set-plays, which caused more chaos in an over-run Norwich defence.
Another fantastic captain's display from Gerrard, who from start to finish showed what it would mean to get his hands on the Premier League trophy.