The Blues were forced to withstand some heavy pressure from the visitors during a goalless first half, but they took the game away from them with goals from Ruben Loftus-Cheek and David Luiz inside the first five minutes of the second half.
Gonzalo Higuain then wrapped up the scoring as Chelsea marked their final home game of the campaign with a win which takes them to the brink of Champions League qualification next season.
The Blues now sit five points clear of both Arsenal and Manchester United - the latter of whom drew with Huddersfield Town this afternoon - and will be guaranteed a top-four spot if the Gunners fail to beat Brighton & Hove Albion.
Chelsea welcomed the likes of Eden Hazard, Higuain and Marcos Alonso back into the starting lineup after Thursday's Europa League semi-final, but despite those fresh legs they still made a slow start to the match as Watford caught them by surprise with a high early press.
The in-form Gerard Deulofeu flashed one low strike narrowly past the post before Troy Deeney - back in the team after suspension - saw a looping header clawed against the woodwork by a fine Kepa Arrizabalaga save after just eight minutes.
Chelsea's early troubles were compounded when N'Golo Kante was forced off with a hamstring injury moments later, being replaced by Loftus-Cheek.
The hosts did ask their first question of the Watford defence in the 14th minute when they made it through the press with a slick passing move which ended with Jorginho attempting to lob Ben Foster, who managed to prevent the ball from floating over his head.
It was a rare moment of reprieve from Watford's relentless attacks in the opening half-hour, though, and both Deulofeu and Jose Holebas should have done better with efforts which missed the target.
Hazard regularly looked the most likely player to make something happen for Chelsea in what could prove to be his final home league game for the club, but he was thwarted by Foster midway through the first half when the Watford keeper plucked the ball off his toe after he had brought it down inside the area.
Chelsea began to grow into the game as the first half wore on and felt they should have had a penalty when Luiz went down under the challenge of Kiko Femenia following a tussle inside the box.
Suddenly it was the home side who looked most like scoring, though, and Pedro twice came close to breaking the deadlock in the final 10 minutes of the half - first curling one shot narrowly past the top corner and then lashing another off target from range after a quick one-two with Higuain.
Despite their positive end to the half it was Chelsea who may have been more relieved to reach the interval still goalless, although that all changed at the start of the second half as the hosts scored twice in the opening five minutes.
Hazard was the creator for both goals to take his assist tally up to 15 - more than any other player in Europe's top five leagues - but he almost got his own name on the scoresheet even before that when he drilled a shot towards goal from a tight angle which Foster needed to tip behind.
The resulting corner was played short and then whipped into the box by the Belgian for Loftus-Cheek, who held off his marker to steer a downward header into the bottom corner.
One quickly became two as Watford were again undone from a set piece, this time Luiz escaping his man to be left unmarked on the edge of the six-yard box and powering a header past Foster.
The scoreline was harsh on the Hornets, but they refused to go down without a fight and Deulofeu came close to pulling a quick goal back when he drilled a shot narrowly wide of the far post.
Chelsea should have added a third shortly before the hour mark when a scramble in the area somehow did not end with the ball in the back of the net, with Foster making a fine save to deny Pedro before Loftus-Cheek could only smuggle the rebound inches off target.
Foster was by far the busier keeper in the second half, but he could do nothing to prevent Chelsea's third when it did arrive 15 minutes from time, with Higuain expertly dinking his finish over the Watford man after latching on to Pedro's through-ball.
It was that cutting edge in the final third which ultimately separated the two sides, although Watford did deserve a consolation goal and almost provided it three minutes later when Holebas clipped the top of the crossbar with only the keeper to beat.
Javi Gracia chose to introduce Isaac Success and Andre Gray with seven minutes left and the duo had the ball in the back of the net within seconds of their introduction, but it was ruled out due to a bizarre offside.
Roberto Pereyra's initial delivery went all the way through and struck the inside of the post, seemingly leaving Success with a simple finish from close range. However, Gray was also in close attendance and Success's header struck his fellow sub in an offside position before going over the line.
It clearly was not Watford's day, although it could have been worse had Olivier Giroud - himself on as a sub - been more clinical on his weaker right foot, passing up two clear chances inside the area in quick succession late on.
Foster was then needed to make a smart save to deny Hazard before keeping out Giroud when he did finally get a shot on target, while Stamford Bridge was also given the chance to bid farewell to the long-serving Gary Cahill after he was introduced as a late substitute.
Chelsea's win lifts them above Tottenham Hotspur into third after Spurs were beaten by Bournemouth on Saturday, while United's shock draw with Huddersfield Town means that now only Arsenal can catch them in the top-four race.
The Gunners are five points behind their London rivals, though, and must realistically beat Brighton in Sunday's later game to stand any chance of finishing in the Champions League places.
CHELSEA (4-3-3): Kepa; Azpilicueta, Christensen, Luiz (Cahill 89'), Alonso; Kante (Loftus-Cheek 10'), Jorginho, Kovacic; Pedro, Higuain (Giroud 79'), Hazard
WATFORD (4-2-2-2): Foster; Femenia, Mariappa, Cathcart, Holebas; Chalobah (Cleverley 67'), Doucoure; Hughes, Pereyra; Deulofeu (Success 83'), Deeney (Gray 83')