Match ends, Ayr United 1, Rangers 6.
Alfredo Morelos and Josh Windass both scored twice as Rangers came from a goal down to thump Ayr United and move into the Scottish Cup quarter-finals.
Ayr took a surprise early lead when Wes Foderingham made a hash of a clearance and Alan Forrest forced the ball in.
Morelos made up for a terrible miss in front of goal with a superb finish.
Quick-fire second-half strikes from Jason Cummings, Windass and Morelos put Rangers in control before further goals from Windass and Jamie Murphy.
Having fallen further behind Raith Rovers at the top League One after last week's home defeat by Alloa Athletic and with their list of experienced absentees growing, Ayr did not have their troubles to seek heading into a game few gave them a chance of winning.
Manager Ian McCall was not even able to be present, the former Rangers winger having received medical advice to stay away following an emergency eye operation on Tuesday.
Rangers counterpart Graeme Murty saw his chance to take advantage and handed Morelos, whose form had dipped after a failed £8m January bid from Chinese club Beijing Rehne, a start up front in a two-pronged attack with on-loan Nottingham Forest man Cummings.
Ayr would have been forgiven for wishing their clearance of pre-match snow off the Somerset Park pitch had not been so successful.
However, as the sun shone brightly, a defence in which former Dunfermline Athletic pair Andy Geggen and Paddy Boyle had been pressed into action despite pre-match doubts about their fitness, restricted Rangers to a speculative Declan John shot wide in the fairly even early stages.
Ayr's growing confidence was sent high into the west coast stratosphere when Foderingham's control deserted him as he tried to collect a David Bates back-pass and, as the English goalkeeper attempted to clear a couple of yards from his goal-line, Forrest slid in to deflect in an unlikely opener.
The 21-year-old striker's seventh goal of the season for the most prolific side in Scottish football added to the family tally for the weekend, older brother James having graced Saturday's 3-2 win over Partick Thistle with a hat-trick for Celtic.
Rangers looked rattled and Foderingham's nerves showed again as he was beaten to a high ball by Lawrence Shankland and Declan McDaid fired the rebound well over.
However, the visitors' greater quality began to tell and Windass should have done better than head against the bar from a James Tavernier cross.
Morelos followed with an even worse miss, firing over from three yards after Greg Docherty's cut-back bobbled unhelpfully in front of the Colombian.
The striker made up for that moments later as a powerful Sean Goss shot thundered against the bar and Morelos showed great skill to half-volley first time into the top corner.
Rangers' growing momentum was interrupted by the half-time whistle and a delay in starting the second half as referee Nick Walsh inspected a pitch being quickly covered by a fresh layer of snow.
The sleet failed to stem the tide of attacks heading Ayr's way once the game did restart, but the League One side threatened on the break as Foderingham did well to block a McDaid shot after coming swiftly off his line.
Murphy had the ball in net after on-loan Wolves goalkeeper Jack Ruddy had blocked a Cummings shot only to be ruled offside, but Rangers killed the game with three goals in six minutes.
Cummings, back to goal, cleverly flicked in a Goss cross following a short corner, Windass finished after Ruddy saved a low John cross with his foot and Morelos tapped in a Murphy cross.
Windass rose to head his second and Murphy fired low into the far corner as Rangers recovered from that early wobble to swagger into the quarter-final draw.
Ayr United assistant manager Neil Scally: "I don't think it was a 6-1 game. I did think there was a potential we could get an upset, especially when we were getting in at half-time still in the game.
"The cup is a free hit for us; our priority is the league. We won't play against teams as good as Rangers every week in the league. If it was good for the boys to measure themselves against them.
"I enjoyed the experience. It was brilliant at 1-0, but at the end of the game it's terrible at 6-1."
- 6GegganBooked at 83minsSubstituted forFauldsat 83'minutes
- 16AdamsBooked at 35mins
- 10ForrestSubstituted forMcGuffieat 75'minutes
- 9MooreBooked at 64minsSubstituted forFergusonat 70'minutes
- 11WindassBooked at 83minsSubstituted forHallidayat 84'minutes
- 26CummingsSubstituted forHerreraat 76'minutes
- 20MorelosSubstituted forMillerat 76'minutes
- Nick Walsh
- Shots on Target
Second Half ends, Ayr United 1, Rangers 6.
Attempt missed. David Bates (Rangers) header from very close range is close, but misses to the right following a corner.
Corner, Rangers. Conceded by Stuart Faulds.
Goal! Ayr United 1, Rangers 6. Jamie Murphy (Rangers) right footed shot from the centre of the box to the bottom left corner.
Attempt missed. Lawrence Shankland (Ayr United) right footed shot from the centre of the box is close, but misses to the left.
Foul by Andy Halliday (Rangers).
David Ferguson (Ayr United) wins a free kick on the right wing.
Foul by Greg Docherty (Rangers).
Stuart Faulds (Ayr United) wins a free kick in the defensive half.
Attempt blocked. Craig McGuffie (Ayr United) left footed shot from the right side of the box is blocked.
Substitution, Rangers. Andy Halliday replaces Josh Windass.
Substitution, Ayr United. Stuart Faulds replaces Andrew Geggan.
Josh Windass (Rangers) is shown the yellow card.
Andrew Geggan (Ayr United) is shown the yellow card.
Goal! Ayr United 1, Rangers 5. Josh Windass (Rangers) header from the centre of the box to the bottom right corner. Assisted by Kenny Miller following a corner.
Corner, Rangers. Conceded by Michael Rose.
Attempt blocked. Kenny Miller (Rangers) left footed shot from the left side of the box is blocked.
Attempt missed. Eduardo Herrera (Rangers) right footed shot from outside the box misses to the right.
Josh Windass (Rangers) wins a free kick on the left wing.