League One Falkirk became the first third-tier side to reach the Scottish Cup semi-finals since 2014 after coming from behind to beat Ayr United.
Dipo Akinyemi put the Championship visitors in front with a clever turn and finish, before Callumn Morrison equalised from the spot midway through the second half.
Kai Kennedy’s deflected long-range strike sent a raucous home crowd into raptures late on, just minutes after Chris Maguire missed a penalty of his own for Ayr.
John McGlynn’s side will now play Inverness Caledonian Thistle at Hampden Park in the last four.
Ayr started the game quickly and deservedly took the lead through their main man Akinyemi, who fired into the bottom corner with the help of a deflection after spinning away from Coll Donaldson.
Lee Bullen’s side probably should have doubled their advantage, but the elusive Akinyemi could not quite stretch far enough to get on the end of Maguire’s fizzed cross.
Falkirk grew into the game as the first half progressed, causing Ayr plenty of problems from set-pieces – Donaldson twice headed off target from Max Kucheriavyi corners.
The home fans may have feared that the half-time whistle came at the wrong time for their side, but their momentum was not interrupted by the break.
Morrison saw a shot deflect agonisingly wide, but roared on by the home fans, the equaliser soon arrived.
Frankie Musonda inexplicably handled in his own box, and Morrison stepped up to smash a confident penalty beyond Aidan McAdams.
The equaliser seemed to spark Lee Bullen’s side into life, with Akinyemi again posing problems – he forced Brian Kinnear into a good save and then rattled the post from close range.
With the pressure building, referee Nick Walsh awarded Ayr a questionable penalty, but Maguire could only hit the upright as he searched for the top corner.
His miss was to prove costly immediately, as Kennedy’s ambitious strike flew into the back of McAdams’ net off the head of Musonda.
Falkirk did not sit on their lead and could have added a late third, but the influential Morrison was denied a second goal by McAdams.
It was a captivating cup-tie, an instant classic, and Falkirk thoroughly deserved their win.
Celebrations at the final whistle were only increased by the news of the draw, which guarantees a lower league side will make the final.
Player of the Match – Callumn Morrison
What they said:
Falkirk manager John McGlynn: “That was amazing. Absolutely amazing. We’ve done it the hard way.
“I’m delighted with the character of the team. It took us about 30 minutes to get in the game. We started the second half really well.
“We’re delighted we’re in the semi-finals. We’ve managed to stay away from Celtic and Rangers.”
Ayr United manager Lee Bullen: “In football, you get so many high highs and low lows. Tonight these players will remember this game as one of their lowest points.
“Credit to Falkirk, good luck to them in the next round. We’re obviously devastated, but we can’t allow this game to define our season.
“We’ve got nine games to go, and we could do something historical for our football club.”
- 6DonaldsonBooked at 80mins
- 15McCannBooked at 86mins
- 10NesbittSubstituted forKennedyat 61′minutes
- 23KucheriavyiSubstituted forYeatsat 82′minutes
- 16WrightSubstituted forOliverat 61′minutes
- 22McKenzieBooked at 45minsSubstituted forBrydenat 87′minutes
- 77MaguireSubstituted forMitchell-Lawsonat 87′minutes
- Nick Walsh