Chelsea: The win, combined with Arsenal's draw against Brighton, means the Blues are guaranteed a top-four finish in the Premier League.
After a quiet first half, Chelsea scored twice within three minutes early in the second period through headers by Ruben Loftus-Cheek and David Luiz.
Gonzalo Higuain sealed the points with a neat finish from Pedro's pass for his fifth goal for the club.
The win moves Chelsea up to third, one point ahead of Tottenham and four points clear of the fifth-placed Gunners.
FA Cup finalists Watford started brightly, going close through Troy Deeney and Gerard Deulofeu, but were left to rue their slow start to the second half that saw Chelsea quickly take the game away from them.
The Hornets, who stay 10th, have now won just one of their past five Premier League games since their FA Cup semi-final victory over Wolves last month.
Chelsea seal top four going into critical week
Chelsea's Europa League semi-final against Eintracht Frankfurt is finely poised at 1-1 after the first leg, but Maurizio Sarri could not afford to rest players as he looked to maintain their push for a top-four finish.
The Chelsea boss says that he wants to treat all his remaining games “with the same importance”.
It is a delicate balancing act for the Italian, who said he left Eden Hazard out of the starting line-up in Frankfurt on Thursday to keep him fresh for their bid to qualify for the Champions League.
Despite the presence of the influential Belgian against Watford, Chelsea began the game sluggishly, with their only shot in target in the first half a chip from Jorginho that was awkwardly palmed away by Ben Foster.
Chelsea also suffered a blow early on when N'Golo Kante was forced off through injury and had to be replaced by Loftus-Cheek.
There was a smattering of boos from the home fans at the half-time whistle. But whatever Sarri said at the break had the desired effect as his side scored two quick-fire goals to take command of the game.
Hazard was the architect of both, his searching cross from the right following a short corner finding the head of Loftus-Cheek, who headed home his ninth goal of the season. Three minutes later, Hazard's corner found the unmarked Luiz, who powered another header past Foster.
Pedro and Higuain both drew smart stops from the Watford goalkeeper before the Argentine finished the game with 15 minutes left, running onto Pedro's sharp through-pass before chipping the onrushing Foster from a tight angle.
With speculation linking him with a summer departure, this could have been Hazard's final Premier League game for Chelsea at Stamford Bridge.
If that is the case then it was a fine way to bow out, though it also gave Chelsea a sharp reminder of what they will be missing if the Belgian leaves.
Gary Cahill was brought on in the final stages for his first competitive appearance since November before his expected departure from the club at the end of the season.