Rangers had to rely on an own goal from Mark Twaddle to give them three precious points at Falkirk. He turned a Dado Prso cross into his own net after 69 minutes for the decisive goal.
Falkirk threatened early on, and Liam Craig lashed a 20-yard shot well wide of the Rangers' goal.
The home side worked hard to deny Rangers space, and the champions struggled to impose themselves on the game.
Falkirk almost gifted Rangers an opener when Jack Ross misplaced a back-header and was glad to see the ball clear the post.
A mistake by Andy Lawrie then presented Nacho Novo with a chance, but Allan Ferguson was down smartly to hold the ball at his near-post.
Rangers were inches away from the opener in the 32nd minute when Prso headed a Steven Smith free-kick against the inside of the post before Craig hooked the ball clear.
It was not the best spectacle with both teams struggling on a threadbare surface and referee Charlie Richmond frequently blowing up for fouls.
Kris Boyd headed Rangers in front after 58 minutes from a Barry Ferguson free-kick but Falkirk hit back. Russell Latapy equalised seven minutes later when he lofted the ball over Ronald Waterreus after Patrick Cregg had sent him clear.
But Twaddle then deflected a Prso cross into his own net after 69 minutes to give Rangers the win.