Rory Loy put the home side in front early on but an own goal from Owain Tudur Jones levelled matters and second-half goals from Dean Shiels and Ian Black won it for the Gers.
The home side took the lead after just five minutes when Steve Simonsen spilled Blair Alston’s shot from the edge of the box into the path of Loy, who coolly slotted home.
That lead was short lived as Rangers got back on terms two minutes later when Jones turned Stevie Smith’s probing cross from the left flank into the roof of his own net.
Northern Irishman Shiels put the Gers in front on 65 minutes when he got behind the Falkirk defence before squeezing the ball past goalkeeper Jamie McDonald.
Falkirk had a decent shout for a penalty when Loy’s shot hit Bilel Mohsni’s hand in the box with a minute left.
The visitors made sure of the win in added time when Black received the ball 20 yards from goal and unleashed a powerful, dipping shot which sailed over McDonald into the net.
Rangers were without their talented youngster Lewis Macleod and on-form striker Nicky Clark after both were injured in the dismal 1-1 draw with Alloa’s part-timers on Saturday.
But the Light Blues had Lee Wallace back after a calf strain ruled him out at the weekend.
Shiels was also thrown into action following four substitute outings as he partnered Kris Boyd up front.
But for the fifth game in a row it was the Scottish Premiership’s record scorer who trudged off with a frown after failing to find the net.