The Warriors had lost all five games played this season, but goals from Colin McMenamin and Alan Cook, as well as an own goal from Rangers goalkeeper Robby McCrorie, saw them prosper against the Ibrox youngsters who pulled a goal back through Ryan Hardie.
Rangers started brightly, but the Warriors had the first chance when Jamie McCormack’s header was saved by McCrorie after six minutes.
Billy Kirkwood’s youngsters failed to heed that warning and, within 60 seconds, McMenamin sent a looping header into the net.
Rangers worked their way back into the game and came close to levelling midway through the first half when a shot from Zak Rudden saw Colin McCabe produce a smart stop.
Jordan Thomson was the next to try and get Rangers level when he sent in a low effort from the edge of the box on 36 minutes, but again McCabe was equal to it.
The hosts built on McCabe’s stop by grabbing a second goal a minute afterwards, with Cook netting directly from a free-kick that he drilled through the wall.
Midfielder Cook was involved in the third goal as well as he let fly from outside the box on 58 minutes and his shot cracked off the underside of the bar , hitting McCrorie on the back before going into the net.
Hardie gave Rangers a route back into the game four minutes later when he found the net after a scramble, but the striker failed to set up a frantic finish as he headed a late chance straight at McCabe.
An extra-time penalty from former Gayfield favourite Paul McManus secured East Fife a 3-2 win over an Arbroath side that led twice.
The game came to life on 34 minutes when Ricky Little headed in a Liam Callaghan corner with Gary Naysmith’s side drawing level 18 minutes into the restart when Jonathan Page to tapped home.
Kane Hester’s effort seven minutes from time squeezed over the line after the keeper had got a hand to it, but Smith levelled with just three minutes left.
McManus netted from 12 yards on 113 minutes after a foul by Jassem Sukar.
The Highland League will be represented in the next round after Turriff got the better of Montrose 1-0 at The Haughs
Turriff won a game of few chances in 59 minutes when Cammy Booth’s corner was met by Andrzej Kleczkowski and he sent a powerful header past Allan Fleming.