Falkirk 0 Rangers 1: Northern Ireland starlet Andy Little claimed his sixth goal of the season as Rangers progressed past holders Falkirk into the third round of the Ramsdens Cup.
The striker's impressive streak continued as he grabbed the only goal of the game after netting his first hat-trick at the weekend.
The win allowed Rangers to take their revenge on the Bairns, who dumped Ally McCoist's men out of the Scottish Communities League Cup last season — with the two sides set to meet again in that competition at Ibrox next week.
Rangers made three changes from the team which fought from behind to secure an emphatic 5-1 win over East Stirling in the Irn-Bru Third Division on Saturday.
Lee Wallace and Ulsterman Dean Shiels both missed out with dead legs, while Dorin Goian was also absent from the team after agreeing a one-year loan deal with Serie B outfit Spezia Calcio.
Brazilian Emilson Cribari and youngster Chris Hegarty both earned their first starts and Barrie McKay was also drafted into the starting line-up.
Little almost opened the scoring early on when he raced onto a Kirk Broadfoot ball only to see his close-range shot blocked by goalkeeper and fellow Ulsterman Michael McGovern.
The away fans then claimed for handball against Chris Smith, as Little again tried to force his way through on goal, but there was no penalty award from referee Calum Murray.
Falkirk had a decent chance of their own when David Weatherston squared across the face of goal for the onrushing Lyle Taylor but he just failed to connect at full stretch in front of goal.
There was another penalty shout — this time for the home side — when Taylor went to ground in the box under pressure from Hegarty but, again, Murray was unimpressed by the pleas.
At the other end, Rangers were threatening when Ian Black curled a free-kick into the box and Francisco Sandaza rose above everyone else in the packed goalmouth only to nod wide.
The breakthrough came on the stroke of half-time when Little collected from Sandaza before driving low past McGovern from a tight angle and into the bottom corner.
Falkirk set about trying to haul themselves back into the tie after the break and Stephen Kingsley picked out Kieran Duffie at the back post but he fired straight into the hands of Neil Alexander.
There was a brief stop in play when assistant referee John Gilmour appeared to suffer a knock but he was able to continue and the match action resumed.
The first booking of the match came with just over 20 minutes to go when Craig Sibbald was cautioned for a challenge on Black.
Rangers then made a double switch when Kevin Kyle and Kal Naismith were thrown into the action for McKay and Sandaza.
The visitors tried to end any hopes of a late Falkirk fightback and a shot from Lewis McLeod was hooked off the line by Blair Alston, after another penalty claim by Broadfoot.
Rangers held on to claim a narrow victory and ensure their names will be in the draw for the next round.
Rangers have signed former France Under-20 international Sebastian Faure on a three-year-deal, subject to international clearance.
The 21-year-old central defender has spent the past week on trial at Murray Park following his release from Lyon in the summer.
Faure was also on trial at Leeds United before arriving north of the border where has impressed Rangers boss Ally McCoist in training.
Faure helped Les Bleus finish fourth in last year's FIFA Under-20 World Cup in Colombia.
Faure is McCoist's sixth summer signing, joining Dean Shiels, Kevin Kyle, Francisco Sandaza, Ian Black and Emilson Cribari at Ibrox.
Faure expressed admiration for the sell-out crowd in Saturday's |5-1 Irn-Bru Third Division victory over East Stirling.
He said: “I am very happy to have signed for Rangers. It is a big club and I have good memories of the club in France.
“The training was good, the players are good and the training centre is great.
“I was in the stadium on Saturday with 50,000 fans and that was beautiful. For me it is incredible because I knew Rangers from my time in France.
“So for me it is very exciting to sign a contract here as a young player.”