Dean Shiels, Lee McCulloch and Barrie McKay netted a double each and Robbie Crawford was also on the scoresheet against Paul Hartley's high-flying Irn-Bru Second Division side.
The Wasps finished the game with 10 men as James Doyle saw red following a challenge on Chris Hegarty on 79 minutes.
Anestis Argyriou and Fraser Aird were both drafted into the Rangers side for the third round tie, with Lee Wallace ruled out with a dead leg and Kyle Hutton dropped to the bench. Shiels, Andy Little and Lewis Macleod were all passed fit to start despite nursing knocks from the clash with Inverness.
Rangers knew they needed a positive reaction following the midweek defeat and they enjoyed the best possible start to the game. An Aird corner broke for Shiels, whose deflected shot found its way through a sea of bodies and into the bottom corner after just two minutes.
It was Shiels who doubled the advantage when he grabbed his second of the day after 21 minutes. McCulloch was the provider with a lovely pass for the Northern Irishman and the offside flag stayed down as Shiels slotted past goalkeeper Scott Bain.
Skipper McCulloch then helped himself to a goal when he unleashed a powerful strike from just inside the box after 33 minutes. The Gers utility man could have netted again just before the break with a ferocious effort that fizzed just over.
Alloa had failed to trouble the Gers defence in the first half but carved out a couple of decent efforts in quick succession after the break. A well-struck free-kick from just outside the area from Nicky Low was comfortably gathered by Neil Alexander. Kevin Cawley then saw his hooked effort curl just past the far post.
Shiels was then denied his hat-trick by the post but any respite for Alloa was brief as Rangers found the back of the net twice in quick succession. Shiels squared into the path of McCulloch and all that was required was a simple tap in from the captain after 72 minutes, before Crawford supplied a low finish from a Shiels cut-back a minute later.
There was worse to come for Alloa when Doyle was dismissed and McKay then added his name to the scoresheet three minutes later with a superb shot from outside the box, before completing the rout with a well struck drive with a minute to go.
- Sports & Recreation
- Lee McCulloch
- Dean Shiels
- Lee Wallace