Kevin De Bruyne was also on target with a sublime free-kick as City responded to Lionel Messi's early strike in remarkable fashion.
City's performance was not only an emphatic response to the 4-0 thrashing in the Nou Camp a fortnight ago that had people questioning manager Pep Guardiola's methods, but reignited their challenge in Group C.
It was a compelling, breathless contest in which both sides created numerous chances against fallible defences.
City had a strong penalty claim turned down early on while Andre Gomes hit the woodwork for Barca. Yet these were just a couple of many memorable moments that contributed to what will be remembered as a classic, and what was perhaps the dawn of a new era for City in Europe.
City started with Sergio Aguero in attack, following his surprise omission at the Nou Camp, and looked all the more dangerous for it.
There was a huge sense of anticipation as the Argentinian broke through a gap, relishing the chance to take on a defence lacking Gerard Pique and Jordi Alba, in the opening minutes.
On that occasion he was flagged offside but it was an indication of City's determination to attack and that same inclination should have yielded a penalty for Raheem Sterling after 10 minutes.
The England forward looked to have been trodden on by Samuel Umtiti as he burst into the area but instead, to widespread disbelief, found himself booked for diving by Hungarian referee Viktor Kassai.
City were sensing another opportunity when Barcelona once again showed their ruthless side to snatch the lead with a clinical counter-attack.
David Silva floated a free-kick into the Barca area and the fit-again Pablo Zabaleta teed up a shooting chance for Aguero. Javier Mascherano blocked and in an instant everything changed as Messi swept the ball forward to release Neymar. The Brazilian raced clear and then played a perfect return pass for Messi behind the retreating defence. Much the same as a fortnight ago, Messi made no mistake as he jinked into the area and finished coolly.
The shock of conceding in such a sudden manner seemed to take the sting out of City for a time and Barca could easily have increased their lead. Neymar had a shot from a tight angle tipped away by Willy Caballero and another effort blocked, while Gomes was also thwarted and Luis Suarez spurned two chances.
But City were gifted a way back into the game six minutes before the break as Sergi Roberto played a casual ball across his own box and Aguero intercepted. He quickly released Sterling and his low ball to the far post was thumped in by Gundogan.
The complexion of the game changed again and Aguero was inches away from getting the final touch to a Fernandinho drive in front of goal.
Both sides committed fully to attack and Messi appealed for a penalty after a Fernandinho tackle before Sterling was let down by a poor touch after being put through on goal.
City's efforts were rewarded after Sergio Busquets bundled Silva over outside the area to give De Bruyne his chance. Barca goalkeeper Marc-Andre ter Stegen made a slight movement in the wrong direction and De Bruyne took full advantage as he lifted the ball over the wall and beyond the German's reach.
Barca were unlucky not to equalise as Gomes rattled the bar following a Suarez break but, in a dramatic passage of play, they were also reprieved as De Bruyne shot wide at the other end seconds later.
The next goal was critical and City got it after another slick attack. De Bruyne released substitute Jesus Navas with a fine throughball and his pull-back struck Aguero before being tucked in by Gundogan. Ter Stegen claimed Aguero had handled but his complaints fell on deaf ears.
It was the goal that killed the game and City held on to celebrate a famous victory.
Nolito believes beating Barcelona tonight is vital to Manchester City's hopes of progressing in the Champions League.
City were beaten 4-0 when the sides met at the Nou Camp a fortnight ago and are now facing a tough battle to qualify for the last 16 from Group C.
Another loss to the Catalan giants could hand impetus to Borussia Monchengladbach or Celtic in what would then be a race for second place.
Forward Nolito, who has scored five goals since his summer move from Celta Vigo, said: "If we want to qualify for the next round we need to win this one.
"We have some difficult games left and the first one is Barcelona. We know how strong they are but we are going to try to take some points off them."
Barcelona will be without two of their first-choice defenders in Gerard Pique and Jordi Alba, while midfielder Andres Iniesta is also sidelined.
Yet they remain a formidable side with Lionel Messi, Luis Suarez and Neymar leading the line.
Nolito, 30, said: "Even if they have players missing it is still Barca we are playing against. They have a very strong squad.
"Whatever player plays can make it difficult for you."
City will have Willy Caballero in goal with Claudio Bravo suspended while top scorer Sergio Aguero seems likely to start after surprisingly being put on the bench in Barcelona.
Nolito said: "I think he is one of the best strikers in the world and we are proud to have him in the team.
"We hope he can have one of those days where he scores many goals and hopefully we can win the match."
City's former Barcelona manager Pep Guardiola is well aware of how ruthless his old team can be and knows the Premier League leaders will have to be at their best.
He said: "We have to play like a final. It's not a final for them, it is a final for us.
"There are just three games left and we dropped two points in Glasgow, so we have to recover those points in the next two games.
"I have never entered a match thinking we can't win but we have to play almost perfectly."
Guardiola has also warned his side to watch their discipline. Bravo's dismissal at the Nou Camp was City's fourth red card in five games against Barca, all of which ended in defeat.
He said: "It's always difficult to win Champions League games and it's always difficult against Barcelona 11 v 11, but when it's 10 v 11 it's almost impossible."
Barca boss Luis Enrique is wary of the threat posed by Guardiola.
He said: "I think Pep's Man City have a lot of things going for them, they can do many things.
"We know Pep and we know his ideas. We have to be very attentive to what they do because Pep will try to touch the correct key to get the result."
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