Strikes either side of half-time from Matt Doherty and Raul Jimenez – who followed becoming Wolves' record signing on Thursday with a stunning volley – put Nuno Espirito Santo's side on the path to a May 18 meeting with Manchester City.
Javi Gracia responded by sending Deulofeu on for Will Hughes and the Spanish winger scored an outrageous chip before Troy Deeney drilled home from the penalty spot in second-half stoppage time.
While Deulofeu's first was special, the one Watford fans will most treasure came when he showed absolute composure to slide home in the first half of extra time and end Wolves' hopes of a return to the FA Cup showpiece after 59 years.
"Since I was young, I followed them. Watford FC, the team for me!— Watford Football Club (@WatfordFC) April 7, 2019
Jonny Castro Otto and Joao Moutinho curled efforts over from 20 yards as Wolves started brightly and they went ahead when an unmarked Doherty nodded Diogo Jota's cross home nine minutes before half-time.
Jimenez struck a fierce shot straight at Heurelho Gomes early in the second half but saved his best for the 62nd minute, controlling Doherty's cross on his chest before acrobatically converting with unstoppable power and celebrating with a Wolves-themed Mexican wrestling mask.
Watford substitute Deulofeu showed the kind of opportunistic finishing his team-mates had lacked when Romain Saiss' poor clearance landed at his feet and he curled exquisitely over John Ruddy 11 minutes from time, igniting the turnaround.
With a historic Wolves victory seconds away, Leander Dendoncker tripped Deeney in the box and the Watford captain smashed a thunderbolt of a spot-kick past Ruddy to force an additional 30 minutes.
Andre Gray's slide-rule pass put Deulofeu through against Ruddy and he guided a precise, low shot past the Wolves keeper and into the bottom-left corner in the 104th minute.
Substitute Ivan Cavaleiro looked sure to take the game to penalties when he rounded Gomes at the death, but he lost control of the ball and Wolves' final chance evaporated.
What does it mean? Gracia cements iconic status
Watford's fans unfurled a gigantic banner depicting their manager before kick-off, displaying the high regard in which he is held at Vicarage Road.
After his side showed incredible spirit and bravery to win at Wembley, an unlikely victory over City next month would render him every inch a Hornets legend.
Deulofeu writes his name into history
Deulofeu became only the seventh player to score a brace in an FA Cup semi-final and his arrival as a replacement for Hughes transformed Watford.
Dendoncker undone by Deeney
Going toe to toe with Deeney is never easy but Dendoncker's challenge on the Watford captain in the dying seconds was ill-advised at best and Wolves' grip on the game was lost as a result.
Key Opta Facts
- Watford won at Wembley for the first time since May 1999 (2-0 against Bolton Wanderers in the second-tier play-off final) - they had lost five of their six games in all competitions at the venue before beating Wolves.
- Since beating Aston Villa in the 1960 FA Cup semi-final, Wolves have been eliminated on each of their last five appearances at this stage of the tournament (1973, 1979, 1981, 1998 and 2019).
- Deeney has scored in both of his FA Cup semi-final appearances – previously doing so against Crystal Palace in April 2016.
- Doherty scored his fourth goal in the FA Cup this season – only Newport County striker Padraig Amond (five) has netted more in the competition in 2018-19.
- Jota has been directly involved in 37 goals for Wolves (26 goals and 11 assists); the most of any player since his debut in August 2017.