A tough task for East Fife became even more difficult as they fell behind after little more than 20 seconds at Ibrox.
Nicky Clark opened the floodgates for Ally McCoist’s side who would net further through a Lee McCulloch hat-trick and a stunning Lewis McLeod strike.
Fifers boss Willie Aitchison said the early goal was a sickener.
He said: “They score and suddenly 45,000 people are up for that, and that’s the problem.
“The plan is to stay composed and keep them quiet and get on to our own game plan, but we waited until the second goal went in for us to start playing a bit.
“We went through a period in the first half just before they got the third when our football was good.
“I said to them at half-time that we were comfortable on the ball, but if we’re going to make mistakes we need to make then up the park and not in front of our goal.”
The supporters inside Ibrox had barely taken their seats when Clark slammed home the opener for the Gers.
East Fife pressed forward themselves, and Liam Buchanan was out of luck when he found himself one on one with the goalkeeper, only for Sebastien Faure to get back and clear.
Rangers always looked dangerous going forward and McCulloch got the first of his hat-trick when he headed home a Lee Wallace cross.
To be fair to Aitchison’s side, they refused to panic and went on to have their best spell of the game.
Buchanan again found space to fire in a strike which was held before Cedric Tuta should have netted but he failed to connect with a cross from six yards.
They were made to pay for their profligacy when McCulloch showed them how it’s done by heading his second.
East Fife gave a debut to former Hearts right back Robbie Neilson, and his failed clearance fell kindly for McLeod who volleyed home a stunning fourth for the home side.
The rout was completed when McCulloch wrapped up the win with another header, this time from a Kyle McAusland cross.
East Fife pressed for a consolation but Neilson’s late drive sailed over the bar.