The pressure was on for the Scottish champions to secure maximum points following Celtic's victory at Hamilton earlier in the day, but they made no mistake and the result ensured Falkirk remain rooted to the foot of the SPL.
Rangers were without Kenny Miller after the striker limped out of the midweek clash at St Mirren with a hamstring strain.
Kirk Broadfoot was dropped to the bench, while Kevin Thomson and Fleck were both added to the starting line-up.
Falkirk drafted Brian McLean and Ryan Flynn into the side following their goalless draw with Motherwell on Wednesday night.
The opening spell failed to yield many real chances and it took a while for Rangers to put their visitors under any pressure.
Nacho Novo tried to unleash a shot from a tight angle which was blocked by Jackie McNamara. From the resultant corner, Danny Wilson forced goalkeeper Robert Olejnik into a decent save with a dangerous header.
The breakthrough came with 18 minutes gone when McLean fouled Kyle Lafferty just outside the box, earning himself a booking. Davis stepped up for the free-kick and deftly lofted the ball over the goalkeeper.
Falkirk tried to hit back when Vitor Lima raced through the middle before teeing up Scott Arfield, but his effort from the edge of the box was comfortably smothered by Allan McGregor.
The Bairns were threatening again when Marc Twaddle's header was blocked on the line, before Flynn's effort on the rebound was punched to safety by the Rangers goalkeeper.
Rangers started the second half strongly and should have been ahead within a minute of the restart. Davis flighted an inviting cross into the box for Lafferty in plenty of space but the big striker nodded over when it looked easier to find the back of the net.
There were more groans from the home crowd moments later when Novo spurned a great opportunity and blasted over with only the goalkeeper to beat.
But, with 57 minutes gone, Rangers were firmly in the driving seat. Lafferty played the ball out to Davis on the right flank and he whipped a lovely ball across the face of goal where Fleck was waiting to slot home at the back post.
Any hopes of a Falkirk comeback were dashed just five minutes later when Davis again turned provider for Whittaker to drill low into the net from just inside the box.
Lafferty had the chance to silence his doubters and put the gloss on the win but saw his effort drift wide of Olejnik's right-hand post.
Then it was Davis' turn to squander the chance to claim his second of the day, when he collected Steven Smith's cut-back from the by-line only to rifle well wide of target.
Smith then had a go himself, after exchanging a one-two with fellow substitute Steven Naismith, with a thunderous shot that was blocked by Olejnik and hit the crossbar on the way over.
Source: Team Talk