Deeney, who was serving a jail sentence for affray when the season started, struck the winner in the seventh minute of injury time.
Seconds earlier Manuel Almunia had saved a penalty which would have sent Leicester through to the npower Championship play-off final.
From Almunia's save Watford broke away and the ball eventually came to Deeney, who crashed home his 20th goal of the season to fire the Hornets into the final against either Crystal Palace or Brighton.
"Manu trains hard and studies penalties, he kept his bottle and kept us in the game," said Deeney. "And as soon as it happened I knew we would score.
"There was no way I was placing it, if the 'keeper had saved it he was ending up in the goal as well.
"Considering the start of the year I had, to score 20 goals and the winner is very satisfying.
"We fancy ourselves against anyone on our day - we'll have a nice night tonight and then get ready for Wembley."
The Hornets' promotion dream looked over when, with the teams tied at 2-2 on aggregate, Marco Cassetti nudged Anthony Knockaert in the area and referee Michael Oliver awarded Leicester a 95th-minute spot-kick.
But Almunia blocked Knockaert's penalty, and the rebound, and moments later Deeney struck the knockout blow.
In scenes reminiscent of Doncaster's breakaway goal to win League One at Brentford a fortnight go - when the same referee gave the Bees a penalty - Watford charged upfield.
Fernando Forestieri swung in a cross from the right and Jonathan Hogg's header back across goal fell to Deeney, who thumped the ball home to spark wild celebrations.
Hornets boss Gianfranco Zola was sent tumbling to the turf as jubilant players, staff and fans charged onto the pitch.
"I probably bruised something but I can't feel it now, probably in the morning," said the jubilant Italian.
"I just lost it, I didn't know where I was going or who I was chasing. I said to myself I had to keep my composure but when it happens you can't control it.
"It was a soft penalty and it would have been unfair to lose on that. Then when I saw the ball travelling towards our strikers I immediately thought of Brentford - I had the movie in my mind.
"It was a good cross, a good header back and the finish from Troy was as good as it could be."
Watford trailed 1-0 from the first leg and twice levelled the tie on aggregate through Vydra, either side of David Nugent's header.
Vydra's first goal, a stunning angled volley, was straight out of the Robin van Persie handbook.
"It was similar to van Persie, or Marco van Basten in the European Championship," added Zola. "It was worth paying for a ticket to see that."