Match ends, Inverness CT 1, Hibernian 2.
Anthony Stokes struck twice as Hibernian recovered from Sunday's League Cup final loss to topple Scottish Cup holders Inverness CT.
The striker netted both first-half goals from close range in the replay to set up a semi-final with Dundee United.
Iain Vigurs replied on 77 minutes, with Carl Tremarco and Liam Hughes missing glaring chances for the hosts.
Hibs then squandered a trio of breakaway openings during a frantic seven minutes of stoppage time.
The bulk of added time came from a confusing period when the visitors were forced to replace goalkeeper Mark Oxley.
Twice Oxley went to ground complaining of an apparent eye problem and was booked for time-wasting, which means he will miss the semi-final, while replacement Otso Virtanen came on for his debut as Alan Stubbs' side were under intense pressure.
The victory ends a run of five matches without a win that has derailed Hibs' Championship challenge and brought Hampden heartache against Ross County at the weekend.
And it takes the number of top-flight scalps the Leith team has taken in cup competitions this season to five.
Stokes had gone seven games without a goal but was well positioned to slam home a shot after the home defence failed to deal with a Lewis Stevenson cross.
Another defensive lapse allowed Liam Henderson to set up Jason Cummings and Stokes was again on hand to tuck in the rebound after Owain Fon Williams had made a good save.
Inverness did not give up their grip on the cup lightly, taking off three defenders over the course of the second half and replacing them with forward-thinking players.
Tremarco failed to convert a back-post opportunity from a few yards, with a slight touch on the ball from Hibs defender Darren McGregor perhaps distracting the full-back.
Some nice skill from Stokes set up John McGinn from a tight angle, with Williams making a good block to keep his side in the game.
A Josh Meekings strike and a Hughes header went close as Inverness pushed for a way back.
The tactic of shelling long, diagonal balls towards captain Richie Foran, making his first start in close to two years, then paid off when his header fell to Vigurs to sweep the ball home.
An equaliser looked certain moments later as Hughes slid in to meet the ball inside the six yard box but somehow the big forward scooped his effort over the top.
Oxley received a bang in that incident leading to the goalkeeper's vision difficulties and after a couple of breaks in play, which infuriated the home fans, Virtanen came off the bench for his first taste of Scottish football.
Vigurs curled a free kick over and a Virtanen fumble presented Meekings with a chance that he could not convert.
With Caley Thistle throwing everything into attack, there were huge gaps for Hibs to exploit in stoppage time, as the exposed Williams made saves to deny Henderson and Stokes, while Cummings shot wide with Stokes well positioned to claim a hat-trick.
Visiting fans, reeling from the disappointment of Sunday's defeat, were put through the mill in those closing stages but now have another Hampden date to look forward to on 16 April.
- 25Fon Williams
- 6MeekingsBooked at 64mins
- 3TremarcoSubstituted forPolworthat 73'minutes
- 17HornerSubstituted forStoreyat 62'minutes
- 15WedderburnBooked at 60minsSubstituted forWilliamsat 62'minutes
- 1OxleyBooked at 87minsSubstituted forVirtanenat 88'minutes
- 2GrayBooked at 83mins
- 19KeatingsBooked at 69minsSubstituted forGunnarssonat 80'minutes
- 9El Alagui
- Stephen Finnie
- Shots on Target
Second Half ends, Inverness CT 1, Hibernian 2.
Gary Warren (Inverness CT) wins a free kick on the left wing.
Foul by Anthony Stokes (Hibernian).
Attempt missed. Jason Cummings (Hibernian) left footed shot from the centre of the box misses to the left.
Attempt missed. Anthony Stokes (Hibernian) right footed shot from a difficult angle on the left misses to the left.
Attempt saved. Anthony Stokes (Hibernian) right footed shot from the centre of the box is saved in the centre of the goal.
Corner, Hibernian. Conceded by Owain Fon Williams.
Attempt saved. Liam Henderson (Hibernian) right footed shot from the centre of the box is saved in the top left corner.
Foul by Ross Draper (Inverness CT).
Jason Cummings (Hibernian) wins a free kick on the right wing.
Attempt missed. Iain Vigurs (Inverness CT) left footed shot from outside the box is too high from a direct free kick.
Josh Meekings (Inverness CT) wins a free kick in the attacking half.
Foul by Darren McGregor (Hibernian).
Substitution, Hibernian. Otso Virtanen replaces Mark Oxley because of an injury.
Mark Oxley (Hibernian) is shown the yellow card.
Foul by Danny Williams (Inverness CT).
(Hibernian) wins a free kick in the defensive half.
Attempt missed. Danny Williams (Inverness CT) header from the centre of the box misses to the right.
David Gray (Hibernian) is shown the yellow card for a bad foul.