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 the game 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.
Shellshocked Wolves settled the quicker at the start of extra time but Watford 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.
"I've said on many occasions that this team has something special," said Watford captain Deeney.
"We're not the most talented, we're not all that, but the hard work and desire at 2-0 down - many teams would've called it a day but we kept fighting and kept going and brought the little man on [Deulofeu], who produced a bit of magic.
"We've got room to grow, there's not a ceiling on us yet as a team. For a club of this size, let's enjoy this moment.
"Manchester City are a formidable team, probably the best team in Europe, but it's a one-off game and we need to come in with belief and know that this hard work can get us a long way."
"It was a tough game, we knew that," said Wolves manager Nuno Espirito Santo. "There is sadness, there is pain but we have to look at it. In the final minutes of the game we should do better because the game was ours.
"Our fans were amazing and we should manage better. We must keep possession of the ball at the end, we had moments where we could have put the game to bed but we did not do that."
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.
Wolves, now able to play on the break, suddenly looked dangerous and Jota nearly doubled the lead minutes later, sprinting down the left before cutting inside and curling a shot just wide.
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 produced a moment of pure inspiration in the 79th minute.
The ball fell to him in the area and he picked his spot, curling delicately over the head of Ruddy into the top corner, leaving the goalkeeper rooted to the spot.
Suddenly the dynamic of the match shifted and Watford were camped inside the Wolves box but they were unable to grab an equaliser despite intense pressure.
But with seconds to go Dendoncker was adjudged to have brought down Deeney in the penalty box and the spot-kick was confirmed by VAR.
Deeney held his nerve and blasted the ball down the middle, with Ruddy unable to keep it out.
That took the game to extra time and Deulofeu applied the killer touch to send Watford through to the final.