The sides were level at the interval after Fernando Forestieri's opener had been cancelled out by a Gabriel Tamas own goal, but the game swung in the hosts' favour after the interval when Giuseppe Bellusci was sent off after bringing down Forestieri in the penalty area.
Troy Deeney dispatched the spot-kick and Forestieri applied the gloss soon after with a fine third.
That looked like it would be the end of the scoring until added-time when Daniel Tozser added the Hornets' fourth from a long-range free-kick before Sam Byram became the second Leeds player to be sent off for an apparent elbow on Daniel Pudil.
Watford started the brighter of the two sides with Forestieri and Deeney having early efforts and their attacking endeavours were rewarded with the opening goal in the 20th minute.
The move was started and finished by Forestieri, who initially did well to bring under a control an over-hit Tozser corner before stepping inside a challenge and laying a pass off to Deeney. The striker back-heeled the ball into the penalty area, Gianni Munari helped it on and, after seeing his first shot saved by Marco Silvestri, Forestieri kept his eye on the ball to head the rebound past the Leeds goalkeeper.
The Hornets continued to look comfortable but a slice of good fortune got Leeds back on terms in the 32nd minute when Billy Sharp's low cross from the right was turned into his own net by the outstretched leg of Tamas, with goalkeeper Heurelho Gomes powerless to do anything about the equaliser.
Having been pegged back, the home side spurned a great chance to retake the lead four minutes later when Almen Abdi's right-sided corner picked out the unmarked Tommie Hoban but he headed over from no more than five yards out.
Both sides had opportunities to take the lead within the first two minutes of the second half; Forestieri curling a shot from the edge of the penalty area just wide before Jason Pearce headed a free-kick narrowly over the top.
But the complexion of the game changed in the 57th minute when a mix-up in the Leeds defence gave Forestieri the opportunity to break on goal, only for him to be fouled from behind by Giuseppe Bellusci.
Referee James Linington had no hesitation in pointing to the penalty-spot before brandishing a red card in the direction of the Italian debutant for denying a clear goalscoring opportunity and Deeney comfortably dispatched the spot-kick.
The excellent Forestieri then made it 3-1 in the 67th minute, latching on to a Munari pass on the left side of the penalty area and evading challenge after challenge as he jinked his way across the 18-yard box before finding the bottom corner via Silvestri's right-hand upright.
Watford added a fourth in injury time when Tozser fired home a superb 30-yard free-kick, before Leeds were reduced to nine men when Byram was shown a straight red card for elbowing Pudil.