First half goals from Olivier Giroud and Willian before a third from Ross Barkley in added time proved to be the difference as the West London club moved back above Manchester United in the race for a Champions League place.
Experienced heads setting the tempo
Frank Lampard made four changes to side that were beaten at The London Stadium in midweek, with Antonio Rudiger dropping to the bench for Kurt Zouma, Reece James replacing Marcos Alonso, Ross Barkley filling in for the injured Mateo Kovacic and World Cup winner Olivier Giroud preferred to Tammy Abraham.
The shape of the game was set very early with Chelsea enjoying 70% of the possession in the first half as Watford kept a deep, compact formation.
The Blues' first real opening came from a counterattack down the left side when in form Pulisic released Giroud who had pulled off of Christian Kabasele, but the 33-year-old's low drive was cleared by the feet of Ben Foster in the Hornets' goal.
Foster could do nothing to stop Giroud's next attempt in the 28th minute as Barkley received the ball in a pocket of space behind Watford's middle block and slotted the ball through to his striker who swept into the far corner.
Watford continued to sit back and Chelsea were awarded a penalty in four minutes before the break when Pulisic was brought down by Etienne Capoue.
Willian took the responsibility, as he had done in the blues' last two league games, and sent Foster the wrong way to give Frank Lampard's men a comfortable advantage to take into the second half.
A comfortable night
Chelsea were in complete control, as Watford struggled to cope with their slick build up play as well as the energy of Pulisic and Mount, but the hosts were unable to create any clear cut chances until the 68th minute,when Willian cut inside from the left and forced a good save from Foster.
As the game reached the final 10 minutes, the visitors began to apply more pressure and substitute Danny Welbeck saw an effort well saved by Kepa after being released down the right side of Chelsea's back four.
Ruben Loftus-Cheek will be dissapointed not to have scored the third goal of the game three minutes from time after a perfect cross from James found his head six yards out, but the midfielder was unable to direct his effort towards goal.
The third did arrive for Chelsea in the second minute of additional time as captain Cesar Azpilicueta received the ball on the byline and cut back to Barkley on the penalty spot, who took a touch before firing into the top corner with his left foot.
What the result means
Chelsea move back into the top four and are once again within one point of third-placed Leicester.
Lampard and his squad travel to Selhurst Park on Tuesday evening for another London derby with Crystal Palace.