Farid El Allagui grabbed a double for the First Division side before Dorin Goian and Nikica Jelavic both netted for Rangers.
However, Mark Millar had the final say with an injury-time winner as Falkirk booked their place in the fourth round.
Rangers manager Ally McCoist suggested beforehand that he may shuffle his pack and he made four changes from the side who defeated Celtic in Sunday's Old Firm derby.
Reserve goalkeeper Neil Alexander - who has started in every League Cup tie over the last two seasons - was drafted into the side for his first appearance this term.
Alejandro Bedoya was handed his first start for the club, along with Lee McCulloch and David Healy, with Allan McGregor, Jelavic and Steven Naismith on the bench and Maurice Edu dropping out of the squad.
Falkirk headed into the tie undefeated in their last eight outings and no doubt aiming to replicate the success enjoyed by Second Division strugglers East Fife against Aberdeen last night.
Rangers were also well aware of the dangers of becoming another high-profile scalp in the competition and started the match strongly at the Falkirk Stadium.
Gregg Wylde tried his luck with a shot from the edge of the area that was high and wide, before McCulloch tested goalkeeper Michael McGovern with an effort from distance.
The visitors continued to push forward in search of the opener and McGovern was called into action again, this time to block a left-foot drive from 20 yards from Bedoya.
However, the best chance of the match so far fell to Falkirk 10 minutes before the break when El Allagui connected with a corner and saw his shot cannon off the body of Wylde on the line, before Rhys Bennett fired wide from the rebound.
David Weatherston then blasted over after finding himself in plenty of space as the home side threatened again.
But there was a nervous moment for the Bairns just before half-time when, with Kyle Lafferty and Bedoya both down injured, Bennett attempted to put the ball out of play and almost fired into the back of his own net instead.
Rangers had a decent chance to open the scoring shortly after the restart when Wylde delivered a teasing ball into the goalmouth for Lafferty but Murray Wallace was able to clear the danger before the Northern Irishman could connect.
Jelavic was thrown into the action after 55 minutes but it was Falkirk who took the lead three minutes later.
Kieran Duffie supplied the cross for El Allagui at the back post and he nodded past Alexander from close range.
Naismith was immediately added to the action for Bedoya and was denied by the post after just two minutes on the park.
The holders pushed forward in numbers and Naismith's header from a few yards out was touched over by the goalkeeper, before McCulloch rifled wide.
Instead, Rangers found themselves caught on the break when Falkirk doubled their advantage after 73 minutes.
Craig Sibbald was the provider on this occasion but the goalscorer was the same as El Allagui connected with a header in plenty of space and nodded past Alexander.
Rangers handed themselves a lifeline when Goian threw himself in front of Steven Whittaker's cross and bulleted home a header with eight minutes to go.
What followed was an intense period of pressure as Naismith was again denied from close range before Jelavic sent a header home from a few yards out after 86 minutes.
But just when the tie looked set for extra time, Millar's shot deep into injury time was touched onto the underside of the bar by Alexander but he could not keep the effort out of the net as Falkirk claimed a dramatic late winner.