Substitute Gerard Deulofeu’s moment of magic sparked Javi Gacia’s side turnaround after they looked down and out late in the game and followed by a penalty from Troy Deeney to pull them level.
A goal from Matt Doherty in the first half and a second-half strike from Raul Jimenez looked had 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.
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.
Nuno Espirito Santo’s Wolves, who reached the semi-final courtesy of a victory against Manchester United will now focus on the league for any chance of European football next season.