Kris Boyd bagged a hat-trick as Rangers saw off East Stirlingshire to set up a Scottish Cup fifth round tie at Hibs.
After a sluggish start, Lee McCulloch slipped a 24th minute shot past keeper Greig Mitchell and Alan Hutton finished off a one-two with Alan Gow soon after.
Gow then set up Boyd to slot home and the same player bagged a second close range goal before half time.
McCulloch found the top corner from 20 yards and Boyd slammed in a penalty to complete a comfortable victory.
The Third Division side never looked like grabbing a goal for their small band of fans in the 34,000 crowd and found the going tough at Ibrox.
"I'm glad it's over," manager Gordon Wylde told BBC Sport.
"It was a fantastic night for us, to play in a great stadium in front a huge crowd.
"We found it difficult to cope with all of Rangers' quality, at times it seemed like they had two or three more players than us."
The breakthrough came when Charlie Adam's chipped pass was collected by McCulloch, who controlled the ball on his right foot before transferring to his left for a composed finish.
Goalkeeper Mitchell did well to block Boyd's angled drive from McCulloch's pass but was left fishing the ball out of the back of the net three times before the half time whistle sounded.
Hutton collected a neat backheel from Gow before sliding a shot home, despite Mitchell getting a touch on the ball.
Jean-Claude Darcheville's pass down the right flank was cut back by Gow into the path of Boyd for a simple finish.
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Darcheville then burst into the opposition penalty area to set up Boyd and the striker's shot clipped a lunging defender to fly in from the edge of the six yard box.
Five minutes after the break, McCulloch slammed in a wonderful strike from 20 yards, with the visiting defence backing away from the Scotland international.
Thomas Buffel was introduced from the bench and almost immediately won Walter Smith's side a penalty.
The Belgian midfielder was impeded by Stephen Oates and Boyd thrashed in a powerful spot-kick to complete his hat-trick.
Buffel, making just his third substitute's appearance this season, went close with a shot that fizzed over the crossbar.
The home side handed a competitive debut to 16-year-old John Fleck and the sub showed a few nice touches in the closing stages against very tired opponents.
"He's got remarkable game intelligence for such a young boy," enthused assistant manager Ally McCoist.
"We went about the game in a professional manner, showed East Stirlingshire the respect they deserved and scored some good goals."
Rangers: Graeme Smith, Hutton, Broadfoot, Papac, Whittaker, McCulloch, Hemdani (Fleck 68), Adam, Gow, Boyd (Naismith 81), Darcheville (Buffel 60). Subs Not Used: McGregor, Cuellar.
Goals: McCulloch 25, Hutton 28, Boyd 30, 45, McCulloch 50, Boyd 62 pen.
East Stirlingshire: Mitchell, Gibb, Kelly (Craig Donaldson 37), Thywissen, Kevin McBride, Brand, McKenzie (Simpson 68), Oates, Brownlie, Ure, Savage (King 83). Subs Not Used: Greg Mitchell, Doyle.
Att: 34,024
Ref: A Crawford
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