Match ends, Hibernian 3, Ayr United 1.
Hibernian stayed on course to retain the Scottish Cup as they fought off the challenge of 10-man Ayr United.
John McGinn curled superbly past goalkeeper Greg Fleming from the edge of the penalty box after seven minutes.
Jason Cummings added a second from the penalty spot after Daryll Meggatt downed Martin Boyle.
Craig McGuffie fired a superb reply, but Ayr's chances were hindered when Scott McKenna was sent off before the break and James Keatings added a third.
It was Hibs' eighth win in 10 Scottish Cup meetings with Ayr but their first in three against Ian McCall's side this season after a draw and defeat in the Championship.
And it takes the Edinburgh outfit into the semi-finals for the third year running - their fifth in six seasons.
More heart in Hibs
This was a completely different Hibs performance from three days ago against St Mirren, when it was lacklustre from the Leith men.
The fluency of passing from the hosts was manifested in the displays put in by John McGinn, Martin Boyle and Andrew Shinnie, who carved their way through Ayr's rear-guard on a regular basis in the first half.
McGinn had lost the brotherly battle on Wednesday against his sibling at the Buddies - Stephen McGinn - but was determined to make up for it back on home turf.
The opening goal started and finished with his good work. Initially, McGinn's skill and back-post cross to Holt was well cleared by Daryll Meggatt, but that clearance ended up finding its way back to McGinn.
From the right side of the box, the Scotland midfielder curled a brilliant effort past visiting goalkeeper Greg Fleming.
The 22-year-old, capped twice, maintained his energetic performance throughout and, on a later surge, the desire he showed to nick the ball beyond Ayr's McKenna drew a late, high, heavy challenge for which the on-loan Aberdeen defender could have no complaints about receiving a red card.
Cummings had much more life about him than was on offer in Paisley too and his 19th goal of the season was calmly despatched - straight as a die - from the spot after Meggatt felled Boyle.
Ayr manager Iain McCall raves about McGuffie and the 19-year-old showed on a bigger stage just why.
It was the Troon youngster's cross that created the winner for Mick Wardrope in the previous round against Clyde.
At Easter Road, McGuffie cranked things up another three of four notches.
As Ayr composed themselves after that early double whammy, Gary Harkins knocked the ball down for McGuffie, who fired a sumptuous half volley into the far top corner from 25 yards for what could be one of the goals of the season.
The winger is certainly now on a lot more people's radar, that's for sure.
A successful defence?
Hibs fans might take a little bit longer to be convinced of Efe Ambrose's sometimes adventurous defending, but the Easter Road side's defence of the Scottish Cup is admirable so far.
The precise Keatings header - that went in off the underside of the crossbar from David Gray's cross - assured the hosts of their place in the semi-finals.
Indeed, Holt almost made it four with another header that was cleared off the line by former Hearts defender Conrad Balatoni.
After waiting 114 years to lift the coveted trophy last year, Hibs might well keep it for a second successive year. They might even play Rangers in the final again.
Hibernian head coach Neil Lennon: "It was an emphatic performance. We could've won by a lot more. I'm very proud and very excited to be taking Hibs to Hampden again.
"But I want to put this out to the fans and players: the most important thing is promotion. Winning the cup last year was massive, but promotion is the be-all and end-all as far as we're concerned.
"We've got the potential to be a very good club - we've got to earn the right to get out of the division, and our last four league games have been below par for some reason. Our two cup games have been fantastic, so we need to address it, and address it quickly."
Ayr United manager Ian McCall: "I'm very proud of the players, supporters and our club. We had an absolute mountain to climb - young McGuffie had a goal of the season contender - but the sending off completely changes everything. We had to give Hibs a lot of the ball.
"In the second half, I didn't think they troubled us that much, but we didn't look a threat to equalise.
"Hibs deserved to win, but there are moments in the match that went against us today. The biggest one was going down to 10 men.
"They gave their all, but ultimately, we're out the cup and we're gutted about that."
- 23ForsterBooked at 17mins
- 6BartleySubstituted forFyvieat 83'minutes
- 9HoltSubstituted forGrahamat 87'minutes
- 35CummingsSubstituted forKeatingsat 77'minutes
- 26McKennaBooked at 45mins
- 23DochertySubstituted forRoseat 68'minutes
- 21McGuffieSubstituted forWardropeat 77'minutes
- 9MooreSubstituted forForrestat 66'minutes
- 12HarkinsBooked at 42mins
- Nick Walsh
- Shots on Target
Second Half ends, Hibernian 3, Ayr United 1.
Foul by James Keatings (Hibernian).
Daryll Meggatt (Ayr United) wins a free kick in the attacking half.
Foul by Brian Graham (Hibernian).
Conrad Balatoni (Ayr United) wins a free kick in the attacking half.
Corner, Hibernian. Conceded by Greg Fleming.
Attempt saved. James Keatings (Hibernian) right footed shot from the right side of the box is saved in the centre of the goal.
Lewis Stevenson (Hibernian) wins a free kick in the defensive half.
Foul by Gary Harkins (Ayr United).
Substitution, Hibernian. Brian Graham replaces Grant Holt.
Attempt missed. James Keatings (Hibernian) left footed shot from outside the box is close, but misses to the right.
Marvin Bartley (Hibernian) wins a free kick on the left wing.
Foul by Brian Gilmour (Ayr United).
Substitution, Hibernian. Fraser Fyvie replaces Marvin Bartley.
Attempt saved. James Keatings (Hibernian) right footed shot from the centre of the box is saved in the top centre of the goal.
Foul by Efe Ambrose (Hibernian).
Gary Harkins (Ayr United) wins a free kick in the attacking half.
Attempt blocked. Grant Holt (Hibernian) header from the centre of the box is blocked.
Goal! Hibernian 3, Ayr United 1. James Keatings (Hibernian) header from the centre of the box to the top right corner. Assisted by David Gray.