London - Gerard Deulofeu starred for Watford as they roared back from two goals down on Sunday to beat Wolves 3-2 and set up an FA Cup final against Manchester City.
Javi Gracia's side looked down and out late in normal time before a moment of magic from substitute Deulofeu and a last-gasp penalty from Troy Deeney pulled them level.
Earlier, a goal from Matt Doherty in the first half and a second-half strike from Raul Jimenez looked like sending Wolves into their first FA Cup final since 1960 in a full-blooded cup tie.
Shell-shocked Wolves settled quickly at the start of extra time but the momentum was with a physical Watford side.
They took the lead for the first time in the match after more brilliance from Spaniard Deulofeu, who rolled the ball past John Ruddy from a tight angle after holding off Conor Coady.
"Everything was lost - we were able to show our character and at this moment I am very proud of my players," said Gracia, who hailed Deulofeu as an "amazing player".
"We tried until the end and sometimes it happens if you believe," he added.
"Today we showed our strength as a squad, our belief. I am very proud."
Both sides are battling to be the "best of the rest" in the Premier League behind the so-called 'Big Six' but on Sunday the focus of both clubs switched to the chance to win rare silverware.
Both sides struggled to find their rhythm during a scrappy opening spell with little in the way of clear-cut openings.
Wolverhampton-born Andre Gray wasted the clearest chance of the game just after the half-hour mark, lifting Deeney's cross over the crossbar from six yards after escaping the Wolves defence.
Minutes later Heurelho Gomes did well to tip over a drive from Leander Dendoncker as Wolves poured forward.
From the resulting corner, the ball was played short to Diogo Jota, who sent over an inviting cross which Doherty headed in to give Wolves a 36th-minute lead.
Gray had another glorious chance to equalise on the stroke of half-time but Wolves captain Coady threw himself in front of a powerful shot to ensure his side went into the break in front.
Wolves gave Watford a mountain to climb when Jimenez - the club's new record signing - hooked the ball past Gomes after controlling a deep cross from Doherty in the 62nd minute.
The Mexico international donned a yellow-and-black wrestling mask as the Wolves fans celebrated wildly.
Watford huffed and puffed as they battled to get back into the game but Deulofeu, brought on in place of Will Hughes in the 66th minute, produced a moment of pure inspiration in the 79th minute.
The ball fell to him in the area and he picked his spot, chipping delicately over the head of Ruddy into the top corner, leaving the goalkeeper rooted to the spot.
With time running out, Dendoncker was adjudged to have brought down Deeney in the penalty box and referee Michael Oliver pointed to the spot after a moment's consideration, with the spot-kick confirmed by VAR.
Deeney held his nerve and blasted the ball down the middle in the 94th minute, with Ruddy unable to keep it out.
That took the game to extra time and Deulofeu applied the killer touch in the 104th minute to send Watford through to next month's final against quadruple-chasing Manchester City.
Wolves manager Nuno Espirito Santo, whose side beat Manchester United in the last round, described "a moment of real pain and disappointment".
"The feeling that we had is that we had it and it got away from us," he said.
"We have to look at it. We have to realise that in the last minutes of the game we should have managed better."
FA Cup semi-final results:
Watford 3-2 Wolves
Manchester City 1-0 Brighton