Goals from John McGinn, Jason Cummings and James Keatings steered Hibs into their fifth Scottish Cup semi-final in six seasons and kept the Easter Road outfit's dream of winning the trophy for a second year in succession very much alive.
McGinn and Cummings, via the penalty spot, in the opening 12 minutes had Ayr United on the ropes but Craig McGuffie threw them a lifeline with a stunning strike before Ian McCall's side were reduced to ten men before the interval, Scott McKenna's reckless challenge on McGinn a red card all day long.,
And 11 minutes from time substitute Keatings ensured there was no way back for Ayr, the striker sending a header in off the underside of the bar.
Hibs had to wait just seven minutes for the opening goal, McGinn's cross taken off the head of Grant Holt by Daryll Meggatt but the midfielder picked up the Ayr defender's clearance to send a superb curling shot from 20 yards past goalkeeper Greg Fleming.
Five minutes later it was two for the Hibees, Andrew Shinnie's terrific crossfield ball taking out Meggatt as he found Boyle who was sent crashing by the Ayr man, leaving Cummings to send Fleming the wrong way from the penalty spot with his 19th goal of the season.
The home side had been in such command they were stunned when Ayr, who had already won and drawn at Easter Road this season, clawed one back in the 33rd minute and what a goal it was. Gary \Harkins cushioned a header down for McGuffie who met the ball 25 yards out to send a thunderous rising shot arrowing past Hibs goalkeeper Ofir Marcian and into the top corner of his net.
Ayr, though, were reduced to ten men a minute before half-time, McKenna giving referee Nick Walsh no option as he caught McGinn at almost waist height with a reckless challenge on the Hibs midfielder.
Hibs came back out looking for that third goal and twice Meggatt came to Ayr's rescue within the space of seconds, sweeping away a dangerous low cross from Cumming with Boyle coming in behind him and then taking the ball off the toes of Efe Ambrose as he looked certain to mark his home debut with a goal.
But Meggatt had Fleming to thank as Boyle's cross crashed off him and spiralled goalwards, the Ayr goalkeeper pulling off an instinctive stop to prevent and own goal before an offside flag denied Boyle.
Keatings had only been on the pitch two minutes before he got that clinching third goal, the little striker hanging in the air to meet David Gray's cross and bullet home a header in off the underside of the bar and former Hearts defender Conrad Balatoni prevented a fourth for Hibs, nodding Holt's header off his own goal-line.
Hibs: Marciano, Gray, Forster, Ambrose, Stevenson, M Boyle, Bartley (Fyvie 83), McGinn, Shinnie, Cummings (Keatings 77), Holt (Graham 87).
Substitutes not used: Laidlaw, McLean, Crane, S Martin.
Ayr United: Fleming, Devlin, P Boyle, Gilmour (Forrest 66), Moore, Harkins, Meggatt, McGuffie (Wardrope 77), Balatoni, Dochert (Rose 68)y, McKenna.
Substitutes not used: Hart, Balfour, McKenzie, Murphy.
Referee: Nick Walsh