Tottenham's 1-0 loss to Bournemouth on Saturday opened the door for Chelsea to go third in the Premier League and they took advantage courtesy of goals from Ruben Loftus-Cheek, David Luiz and Gonzalo Higuain.
The Blues were under pressure for much of the first half and lost midfield enforcer N'Golo Kante to a muscle injury after 10 minutes, making the Franceinternational a doubt for their Europa League semi-final, second leg against Eintracht Frankfurt on Thursday.
The recalled Eden Hazard assisted goals for Kante's replacement Loftus-Cheek and David Luiz in the space of three second-half minutes, before Gonzalo Higuain rounded off the scoring as Chelsea edged closer to a top-four finish.
Watford started on the front foot and Troy Deeney had a header pushed onto the post by Kepa Arrizabalaga in the eighth minute, while Kante's injury gave the Blues more cause for concern.
Chelsea were a different side after the break and moved ahead in the 48th minute when Hazard picked out Loftus-Cheek to head home.
David Luiz evaded Adrian Mariappa to nod another Hazard delivery past Ben Foster as the Blues turned the game on its head.
Foster produced a pair of strong saves to keep Pedro and Higuain at bay, but he was helpless when the duo combined and the on-loan Juventus striker dinked in a fine finish.
Watford were denied a consolation in bizarre fashion when Roberto Pereyra's free-kick hit the post and substitute Isaac Success headed in the rebound off an offside Andre Gray.
Club captain Gary Cahill was sent on to a rapturous ovation in the 89th minute for a final appearance at Stamford Bridge before departing when his contract expires at the end of the season.
Sarri's Hazard gamble pays off
Eyebrows were raised when Hazard was listed among the substitutes for the Europa League semi-final, first leg against Eintracht in midweek, but the Belgian looked fresh as he helped inspire a potentially crucial win for Chelsea.
The winger's darting runs and exceptional vision proved the undoing of Watford in what could prove to be his final home match as a Chelsea player amid persistent links to Real Madrid.
Should Hazard depart in the close season, Maurizio Sarri faces a huge task in finding an adequate replacement.
