Wolves looked like they were heading for their first FA Cup final appearance since their triumph in 1960, but they squandered a 2-0 lead to Watford and eventually lost 3-2 to the Hornets after a remarkable comeback sparked by Gerard Deulofeu.
Matt Doherty opened the scoring for Nuno Espírito Santo's men before Raul Jimenez doubled their lead in the 62nd minute on Sunday.
However, second-half substitute Deulofeu hit back with a beautiful chipped finish in the 79th minute before Troy Deeney's last-minute penalty sent the tie into extra-time.
Deulofeu then popped up with a brilliant second, scoring the winner after skipping past Wolves defender Conor Coady before slotting it past John Ruddy in goal.