Anthony Knockaert missed a 97th-minute penalty before the hosts ran up the other end to secure a spot at Wembley on May 27 after Matej Vydra had netted either side of half-timeTroy Deeney's 98th-minute winner booked Watford's place in the Championship play-off final after Leicester City missed a penalty moments beforehand.
Deeney smashed home Jonathan Hogg's headed centre seconds after Anthony Knockaert had passed up the opportunity to win the tie for his own side when Manuel Almunia saved his penalty.
Matej Vydra had levelled the aggregate score in the first half before David Nugent put Leicester back in front, but Vydra looked to have forced extra time with his second goal before Deeney's remarkable strike.
A David Nugent goal in the first leg left the home side with a one-goal deficit to overcome if they were to reach Wembley on May 27, and Vydra came within inches of levelling the aggregate score inside seven minutes when he ran onto Deeney's through ball but directed his shot wide from 12 yards.
The Czech, though, made amends soon after with a sensational volley from inside the penalty area. Marco Cassetti sent a lofted cross forward that Vydra watched drop over his shoulder before connecting with the ball first time and sending it looping over Kasper Schmeichel.
The opening stages were dominated by the London side, but Watford could only enjoy parity for four minutes as Nugent spun away from Lloyd Doyley to meet Knockaert's whipped corner and arrow a header down for the equaliser on 19 minutes.
The game tempered out to a much more equal affair thereafter, with both sides exchanging goalscoring opportunities.
Deeney ran through to test Schmeichel moments after Nugent's header, but the goalkeeper was quick off his line to smother before Knockaert fired high and wide when in a good position at the other end.
Leicester showed more urgency after the break, with Ritchie de Laet and Lloyd Dyer causing the hosts a number of problems down either flank as Watford retreated to potshots from distance in the opening exchanges.
The Hornets, though, could - and perhaps should - have again retaken the lead on the day when Almen Abdi's low drive from the edge of the area was flicked around Schmeichel's right-hand post via the heel of Michael Keane.
That close call reenergised Watford and man-of-the-moment Vydra - who had gone 13 games without a goal ahead of kick-off - coolly finished off a fine team goal to again level the aggregate score, with Deeney again notching the assist after a smart one-two.
Deeney thought he had handed the hosts a spot at Wembley just minutes later when he converted low past Schmeichel, but his celebrations were quickly, and correctly, cut short by the assistant referee flagging for offside.
As the game ambled into stoppage time, an injury to Joel Ekstrand and Knockaert saw the clock run past the four allocated minutes, and Leicester were awarded a 97th-minute penalty when Cassetti appeared to haul down Knockaert.
The midfielder brushed himself down to take the spot-kick, but saw Almunia save both the initial effort and his follow up with his feet.
Watford immediately countered, and to devastating effect. Ikechi Anya marched up the right flank to allow Fernando Forestieri to send an arrowed cross over the Leicester defence. Hogg headed the ball into the path of Deeney, who hammered home from 12 yards to send his side into the play-off final.