The Ibrox side put memories of their League Cup defeat behind them as Dean Shiels, Lee McCulloch, Robbie Crawford and Barrie McKay helped an emphatic claim victory
The Ibrox side made easy work of in-form Second Division outfit Alloa in order to join the SPL sides in the next round of the tournament.
Ally McCoist made two changes from the team that lost in the League Cup to Inverness CT, with Anestis Argyriou and Fraser Aird replacing Lee Wallace and Kyle Hutton.
Alloa boss and former Hearts and Celtic midfielder Paul Hartley gave starts to Darren Young and Kevin Cawley in place of Martin Grehan and Mitch Megginson from the team that defeated Albion Rovers last Saturday.
The home side banished the memories of midweek within the first five minutes when a corner from the left by Aird was not cleared by the Alloa defence and that allowed Shiels to rifle the ball beyond Wasps keeper Scott Bain.
Rangers continued to pile the pressure on the visitors with Andrew Little and Chris Hegarty both having efforts at goal, but neither could find a way past Bain in the Wasps goal.
But the second goal came shortly afterwards, as Hegarty played the ball in from the left-hand side to McCulloch, who in turn found the run of the onrushing Shiels, who made no mistake as he powered the ball into the Alloa net.
The Ibrox side extended their lead further when Jason Marr surrendered possession to Little in the middle of the Alloa half and that allowed Shiels to break forward and play in McCulloch for Rangers' third of the game.
Alloa had the first chance of the second chance as Nicky Low won a free-kick on the edge of the area and the young winger took the set piece himself, but luckily for the home side Neil Alexander was able to get behind the ball to save comfortably.
Northern Ireland international Shiels should have claimed his hat-trick as he was put in on goal by substitute McKay, but the former Kilmarnock forward’s strike was saved onto the post by Bain and the rebound which fell to McKay was deflected away by an onrushing Alloa defender.
Rangers continued their rampage as substitute Crawford played in Shiels on the right-hand side of the box and the forward turned his man before giving the ball to McCulloch six yards out to tap home his side’s fourth.
Four then turned to five with a quarter of an hour left as Crawford and Shiels played the ball together before the young substitute claimed his first goal of the game.
Things became even worse for the visitors as Michael Doyle was sent off for a challenge on Hegarty to leave the Wasps a man down.
McKay was the next to get a goal for the Ibrox side as he cut inside from the left wing and curled a 25 yard effort beyond the helpless Bain in the Alloa goal.
With minutes remaining McKay claimed his double as he stroked the ball home from just inside the box to seal the cup passage