East Fife 0 Rangers 4
The third division leaders were promised a holiday in Barbados for winning, but an Ibrox side without the likes of Barry Ferguson, David Weir and Allan McGregor were never in danger.
The Fifers did start brightly and Paul McManus forced Roy Carroll into a hurried clearance inside two minutes.
Kris Boyd volleyed wide in six minutes with East Fife appealing for offside, but a Greig McDonald cross forced Ugo Ehiogu to head clear at the other end.
Just as the Fifers looked to pose a threat a moment of slackness cost them dear.
No-one picked up Nacho Novo from Kirk Broadfoot's throw-in and from 25 yards the Spaniard hammered a shot past William McCulloch in 13 minutes.
Rangers almost conceded an immediate equaliser, but Ryan Blackadder's dipping effort bounced off the top of the bar.
Broadfoot miscued horribly to send an effort sailing into the stand, but played a vital part in the second goal after 34 minutes.
It was his shot that was blocked by McCulloch's leg but the ball fell kindly for Boyd to tap in the rebound.
Novo had an angled drive pushed round the post in 46 minutes while Kevin Gordon hurried an effort straight into Carroll's arm seconds later.
Carlos Cuellar then thumped a header into the net in 54 minutes from Charlie Adam's corner and Rangers got a fortunate penalty in 65 minutes.
Jonathan Smart seemed to win the ball clearly against Thomas Buffel, but ref Willie Collum pointed to the spot and Boyd made no mistake.
Chris Burke almost sealed the win with a glorious solo effort in 73 minutes but his efforts shaved the post.
McCulloch had the last say in a one sided match when he brilliantly tipped over a Buffel drive which was headed for the top corner.