A howler by Watford defender Samir allowed Rodrigo to double United's lead after Raphinha had put Leeds ahead with a stunning first-half strike.
Whites winger Jack Harrison, assisted by 20-year-old substitute Sam Greenwood, inflicted further misery on the Hornets with a third goal, ensuring Leeds took all three points back up the M1 with them.
The result took the Whites nine points clear of the Premier League drop zone, with 18th-placed Burnley set to take on fellow strugglers Norwich City on Sunday afternoon.
Graham Smyth, the YEP's chief football writer, hands out the scores.
1. Illan Meslier
6 - Some important interventions from set-pieces in particular as Watford tried to target him with in-swingers. Photo by Alex Morton/Getty Images.
2. Luke Ayling
5 - Watford targeted the flanks and Ayling found himself scrambling at times. Had to dig in and did so. Photo by BEN STANSALL/AFP via Getty Images.
3. Liam Cooper
8 - The best player on the park for a long time. Mopped up so many attacks, snuffed out danger. Deserved the clean sheet. Photo by BEN STANSALL/AFP via Getty Images.
4. Diego Llorente
5 - Some poor decisions on the ball, some poor defending and some good bits of defensive play. Photo by Henry Browne/Getty Images.
5. Stuart Dallas
5 - Was left to do a lot of defending and isolated at times. Watford found joy getting behind him. Like Ayling, dug in. Photo by Henry Browne/Getty Images.
6. Mateusz Klich
5 - Couldn't get much going. A few nice moments aside, there was no control in the middle for Leeds. Photo by BEN STANSALL/AFP via Getty Images.