Rangers set up a Scottish Cup fifth-round date with Kilmarnock but only after a less than convincing display in their 3-1 win over Cowdenbeath.
It all looked to be going so smoothly for Steven Gerrard's side at Central Park as goals from Andy Halliday, Lassana Coulibaly and Kyle Lafferty meant they went in at half-time with one foot in the last 16.
But on a ground that doubles as a stock car venue, the Ibrox men were not at the races after the break and allowed David Cox to pull one back for Gary Bolan's part-timers.
There were a couple more scares after that but Gerrard was relieved to see his side avoid a mortifying slip-up as they confirmed their February 9 trip to Rugby Park.
The tie was originally scheduled for January 18 only to be called off just three hours before kick-off as temperatures plunged in Fife.
This time Gers chipped in with their League Two hosts to pay for a heated dome that ensured the re-arranged fixture beat Scotland's latest cold snap.
Having seen fellow top-flight sides Dundee and Motherwell crash out to lower league rivals, Gerrard knew the dangers of being caught cold early on.
Lafferty was brought back in to partner Jermain Defoe up front as top-scorer Alfredo Morelos was given the night off.
But even without the Colombian Gers were too hot for Cowden to handle early on and took the lead after just 12 minutes.
Blue Brazil defender Jason Talbot went down clutching his knee after a tussle with Lafferty in the corner and with the home side momentarily down to 10 men, Gers pounced.
Defoe set the ball back for Halliday, who sold Kyle Miller with a dummy before drilling home from 20 yards out.
Bolan's side survived a clear penalty shout when Fraser Mullen used a hand to stop Lafferty's knock-down but the game was up on 26 minutes as Coulibaly fired in Rangers' second.
Lafferty got his head to a Steven Davis corner, flicking towards Defoe at the back post. The former England hitman's strike was blocked by Blair Malcolm but there was no one free to halt Coulibaly ramming home the loose ball.
Lafferty then grabbed his first goal since September on the stroke of half-time, out-pacing Jamie Pyper to get on to Ryan Jack's through ball before prodding past David McGurn.
The mercury dipped below zero during the interval and it showed as Rangers froze from the restart, gifting Cowdenbeath an unlikely lifeline.
Kris Renton's charge through the middle forced Jon Flanagan into a clumsy trip. The tackle appeared to be just outside the box but referee Craig Thomson pointed to the spot.
Wes Foderingham guessed correctly as he kept out Harvey Swann's spot-kick but was helpless as Cox bundled in the rebound.
And Light Blue hearts were in mouths after 67 minutes when Halliday's short pass back gave Robbie Buchanan all the encouragement he needed to press down on Foderingham. Both the opening goalscorer and his keeper were relieved to see the ball smash off the Cowden forward then bounce wide.
It was lacklustre stuff from Gerrard's team and they had to rely on an offside flag denying Jordan Allan from grabbing another for Bolan's side after a Flanagan blunder.
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