The result takes 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.
With the game's huge consequences impossible to ignore, nerves were evident from the first kick at Vicarage Road as the game got off to an edgy start.
The home side were pepped by a pair of promising kicks awarded by referee Andre Marriner for fouls against Hornets midfielder Juraj Kucka. The first, delivered by Imrân Louza, cleared the wall and whistled wide of the post, before Cucho Hernandez gave Illan Meslier a scare with a whipped-in shot which the Frenchman was forced to swipe away for a corner.
Raphinha broke the deadlock for Leeds in the 20th minute at Vicarage Road. The winger charged toward the goal and tried to play a one-two with Dan James. The ball ricocheted between the Welshman and the Hornets' defenders and eventually found its way back to Raphinha, who rifled it past Watford 'keeper Ben Foster from the edge of the area.
Meslier made a fine save to prevent clean-through Ismaïla Sarr late in the half, but the winger was flagged offside anyway, sending the teams down the tunnel with the score at 1-0.
The Hornets began the second half very much on the front foot and the visitors, overran, were soon struggling to leave their own half.
Sarr squandered a golden opportunity to level for Watford around the hour mark. The winger beat Stuart Dallas to João Pedro's through ball to earn a clear sight of goal. He took a touch, but couldn't wrap his foot around it, sending his shot flying into the stands.
As the game descended into an out-of-control end-to-end spectacle, the home side roared to will their players to find an equaliser before Watford defender Samir gave cause for some of them to head for the exits. Greenwood's through-ball rolled beyond its target player Rodrigo, and into the path of Hassane Kamara who guided the ball toward his defensive teammate but Samir miscontrolled it. Rodrigo pounced, playing it round Foster to double the Whites' lead.
Harrison put the result beyond doubt in the 84th minute. Greenwood played Harrison in on the left hand side of the box where the winger struck it cleanly across goal. The sight of the ball bulging the far side-netting was enough to send a good number of the patient Vicarage Road faithful toward the stadium exits.
Watford XI: Foster, Femenia, Kabasele, Samir, Kamara, Louza, Sarr, Sissoko, Kucka (72 - Kayembe), Hernandez (38 - Dennis), Joao Pedro (81 - King).
Unused subs: Bachmann, Cleverley, Masina, Cathcart, Kalu, Sierralta.
Leeds XI: Meslier, Ayling, Llorente, Cooper, Dallas, Klich (58 - Phillips), Koch, Raphinha (82 - Summerville), Rodrigo, Harrison, James (67 - Greenwood).
Unused subs: Klaesson, Struijk, Gelhardt, Hjelde, Cresswell, Kenneh.