United's Brazilian star Raphinha fired Leeds ahead with a neat finish from the edge of the box in the 21st minute and Jesse Marsch's side took a 1-0 lead into the break.
Early Watford pressure at the start of the second half then no doubt caused some nervous moments in the away end but the Whites doubled their lead in the 73rd minute as record signing Rodrigo netted in front of United's delighted fans.
The Spaniard wheeled away to celebrate with the visiting contingent who still had one final treat in store as Jack Harrison bagged United's third goal with five minutes left.
Here are ten pictures of the delighted fans in the away end as well as Leeds celebrating their success.
1. Opener
Raphinha, left, celebrates putting Leeds United 1-0 up with Stuart Dallas, right, but down the opposite end of the pitch to the traveling Whites contingent. Photo by BEN STANSALL/AFP via Getty Images.
2. Elation
As Rodrigo puts Leeds United 2-0 up at Watford, shortly after Watford had squandered a fine chance to level through Ismaila Sarr.
Picture by John Walton/PA Wire.
3. Get in!
Rodrigo celebrates his strike in front of United's delighted travelling fans. Photo by BEN STANSALL/AFP via Getty Images.
4. Sheer joy
As Rodrigo makes it 2-0 to the Whites. Photo by BEN STANSALL/AFP via Getty Images.
5. Massive victory
Jack Harrison, centre, celebrates in front of the delighted away end along with Sam Greenwood, left, and Raphinha, right.
6. Job done!
Jack Harrison, centre, celebrates his strike with substitute Crysencio Summerville, right, as Sam Greenwood, left, shows his delight too. Photo by Alex Morton/Getty Images.