The recalled Matej Vydra was the hero for the Hornets, netting twice in the second period with both he and fellow striker Troy Deeney creating havoc on the restart.
It was all a far cry from the first-half when a gift of a goal from the recalled Billy Sharp and a magnificent half-volley from Rudy Austin - his third strike of the campaign - put United 2-0 up after just 19 minutes as the visitors toiled.
But Slavisa Jokanovic’s side belatedly got their act together, with Troy Deeney pulling one back on 39 minutes and he played his part in setting up Vydra for a smart leveller on 56 minutes.
After levelling matters, the Hornets proceeded to dominate most of the second period and their comeback was completed nine minutes from time when Vydra bundled home the winner.
It was a harsh lesson for Leeds, who produced a high-octane first 35 minutes, but to their credit, Watford moved through the gears in the second half and looked a real potent attacking force.
Neil Redfearn made two changes to his starting line-up, with Sharp and Sam Byram coming in for Steve Morison and Casper Sloth respectively.
Both made their mark during the first period, with Watford not at the races for large parts of the opening 45 minutes, with Leeds, in contrast, right on top of their game.
An accomplished showing, with Leeds wreaking havoc at times yielded two goals, one gifted to them and the other simply sublime.
The visitors looked a poor imitation of a side in contention for promotion, with their implosion to provide United’s opener on a plate on seven minutes summing up their abject half.
A through-ball from Luke Murphy did not offer too much danger with Ikechi Anya covering the danger, but a lack of basic concentration saw his header almost fly past ex-Spurs keeper Heurelho Gomes, who got only parry the haphazard connection, with Sharp obligingly tucking the ball into the empty net for a tap-in.
It was the fourth goal of the campaign for Sharp, making his first appearance for the Whites since February 7, and his 150th in his career.
Watford failed to dust themselves and regain their composure and looked porous at the back, with Anya looking a particular weak line at left-back.
A spell of pressure ended with Lewis Cook’s drilled low shot held by Gomes before United went 2-0 up on 19 minutes with a peach of a strike.
A poor clearance from Anya was latched onto by Austin, who unleashed a stunning 30-yard half-volley which flew past Gomes in a real contender for goal of the season.
It was no more than United, who had conceded 17 goals in their previous five matches with Watford, deserved and it was they who resembled the promotion-chasers, not Watford.
Vydra, starting in place of the injured Odion Oghalo, who had netted 14 times in a goal-laden run in his previous ten games, fired over into the Kop, with the off-beam effort summing up the visitors’ lacklustre opening half-hour.
The Hornets’ first serious threat eventually arrived when Deeney supplied the overlapping Juan Carlos Paredes, whose low shot was saved by the legs of Silvestri, with Sol Bamba diverting the loose ball into his arms.
But the visitors provided themselves with a lifeline on 39 minutes by pulling a goal back from a familiar source.
A fine defence-splitting pass from Vydra found his strike partner Deeney, who raced clear before coolly firing the ball low past Silvestri - for his 14th goal of the season and sixth against Leeds in five outings.
The goal provided Watford with a transfusion of confidence and they were on the top for the final spell of the half.
Smart defending from Bamba soon denied a certain goal from Vydra following Miguel Layun’s dangerous low cross, the final significant action of an entertaining half.
Leeds proceeded to start the second half with the same sense of urgency and intensity as they fid in the first period and went desperately close to a third goal in a whirlwind 60 seconds.
First, Sharp delivered a great pass to the rampaging Austin but Gomes raced out to block his effort, with the Jamaican’s follow-up cleared off the line by substitute Gabrielle Angella, who had entered the fray towards the end of the first half for the injured Joel Ekstrand.
Moments later, Sharp almost got on the end of a dangerous Austin cross before Murphy saw his curling lob fly over.
But the next development in the game was a telling one at the other end, with the Hornets restoring parity with a quality leveller.
A lovely touch in midfield from Almen Abdi found Deeney with a classy exchange between him and Vydra culminating in the Czech-born striker tucking the ball home with Leeds being defensively undressed.
Vydra raced clear minutes later as Watford scented blood, with his shot was parried smartly by Silvestri, with the Hornets starting to boss proceedings and swarm forward in numbers with Vydra and Deeney increasingly influential.
Leeds had to withstand a fair bit of pressure and survived a mini-scare when Ben Watson dragged a shot wide, with Watford looking the side most likely to score next.
A weak shot from Alex Mowatt, easily gathered by Gomes, was an effort in isolation with Watford going desperately close to a third on 71 minutes when Deeney found Abdi, whose low angled shot flew inches wide.
Increasingly under pressure with Deeney and Vydra running the show, Leeds’ defence buckled on 81 minutes when Deeney played in Vydra and despite his initial shot being blocked by Silvestri, the striker was on hand to scramble home the rebound.
Leeds United: Silvestri, Wootton, Cooper, Bamba, C Taylor, Murphy, Austin (Adryan 74), Cook, Mowatt (Antenucci 84), Byram (Cani 90), Sharp.
Substitutes unused: S Taylor, Berardi, Sloth, Walters.
Watford: Gomes; Paredes (Hoban 90), Ekstrand (Angella 42), Cathcart, Anya; Layun (Munari 52), Watson, Tozser; Abdi; Deeney, Vydra.
Substitutes unused: Bond, Pudil, Motta, Forestieri.
Referee: A Haines (Tyne and Wear).
Attendance: 24,705.