Coventry scored twice deep into stoppage time to stun Wolves 3-2 at Molineux and reach the FA Cup semifinals for the first time since they won the competition in 1987.
The Championship side looked to have blown their chance to reach Wembley when Wolves themselves scored twice in the final seven minutes of the 90.
However, Ellis Simms' second goal of the match levelled in the 97th minute before he teed up Haji Wright to fire into the corner three minutes later.
"Immensely proud. It's really hard to put into words really," said Coventry boss Mark Robins.
"It's been a long time since it's happened and the fact we were not only a goal down but we'd got back into it and went on to win it and deservedly so.
"We showed real courage, real determination and the finishes were outstanding as well."
The home side were without all of Gary O'Neil's preferred front three of Pedro Neto, Hwang Hee-chan and Matheus Cunha due to injury.
"I knew it would be tough as it was. We have one fit senior attacker at the club," said O'Neil.
"Losing in a quarterfinal is obviously a missed opportunity, we produced as good as we could produce. That was it, the lads gave everything."
Simms has now scored 10 goals in his last eight games, but got some fortune for his controversial opener.
The ball rebounded off the former Everton striker from Liam Kitching's header across goal eight minutes into the second half and was allowed to stand despite a check for handball against the Coventry frontman.
DRAMATIC ENCOUNTER
Wolves goalkeeper Jose Sa then crucially kept his side in the tie with a string of vital saves, while Kasey Palmer should have scored when he curled inches wide.
It looked like the Sky Blues would be made to regret those missed chances when Rayan Ait-Nouri pounced on an error from Joel Latibeaudiere to smash home the equaliser.
Ait-Nouri then set up his fellow left-back Hugo Bueno to fire into the bottom corner for his first senior goal.
Yet, the drama did not end there as Bobby Thomas' flick-on found Simms unmarked to bullet in a header.
Just as both sides were preparing for an extra 30 minutes, Coventry then struck in the 100th minute to snatch victory.
Simms again played a big part as he picked out Wright at the edge of the box and the American international curled an unstoppable effort into the far corner.
A founder member of the Premier League, Coventry sank from the top down to the fourth tier of English football as recently as the 2017-18 season.
But they have achieved two promotions under Robins and narrowly missed out on a return to the Premier League last season, losing the Championship playoff final to Luton on penalties.
Wembley awaits once more in the last four potentially against the likes of Manchester City or Liverpool.
City continue their quest for another treble in their FA Cup quarter-final at home to Newcastle later on Saturday.
Liverpool travel to Manchester United and Chelsea host Leicester in the other quarter-final ties on Sunday.