On the park, Falkirk almost took the lead when Wheatherston's shot came back off the post and Rangers goalkeeper Neil Alexander struggled to deal with a cross by Lyle Taylor moments later.
Rangers responded with McCulloch flashing a shot wide from the edge of the box.
However, the former Wigan player did find the net on 18 minutes, powerfully nodding Ian Black's corner past Michael McGovern.
Sebastien Faure almost marked his Rangers debut with a goal, McGovern blocking the Frenchman's long-range shot before tipping over a Little header.
Dean Shiels, back after a two-game injury absence, was the architect of Rangers' second, superbly laying on the pass for his Northern Ireland teammate Little to finish.
Interview - Rangers manager Ally McCoist
Blair Alston had a shot saved as Falkirk bid to reduce their arrears and Taylor's 30-yard free-kick early in the second half drifted wide.
And McCoist's men made sure of progress to the next round when McGovern came off his line to retrieve McCulloch's lofted ball but the keeper was left stranded after an intervention by Chris Smith and McCulloch profited with a composed finish.
Youngsters Barry McKay and Robbie Crawford as well as experienced forward Kevin Kyle made appearances from the bench as Rangers withdrew Shiels, Faure and Lewis MacLeod.
And Kyle created a chance for Little with a headed knock-down but the club's top scorer chipped too high with the goal at his mercy.
Rangers manager Ally McCoist:
"Miles better, no comparison. I was really disappointed at the way we passed the ball and performed in Berwick. Tonight was a lot better.
Interview - Falkirk manager Steven Pressley
"Some of the passing was excellent but I still believe we can do better when we've got the ball.
"The most pleasing aspect of our game was getting the ball back, closing down and hunting in packs. I thought we were excellent at that and I thought we deserved to win the game."
Falkirk manager Steven Pressley:
"My players gave me absolutely everything.
"We just lost goals at key moments. We created a couple of really good opportunites, we hit the inside of the post.
"After that good start, we lost a goal to a set play and that gave Rangers confidence."
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