Joao Pedro was also on target from the penalty spot and although Stoke's Nick Powell made it 2-2 in the 81st minute, Sarr had the last word to lift the Hornets into the play-off positions.
Stoke will take some convincing, however, that the goal which cancelled out Steven Fletcher's second-minute opener midway through the first half – credited to Tom Cleverley – was not a major miscarriage of justice.
It took the Potters all of 90 seconds to take the lead from a cleverly-worked short corner routine that ended with Powell setting up Fletcher from close range.
The game's controversial moment arrived in the 28th minute in the shape of Watford's puzzling equaliser.
Cleverley's rising drive from just inside the box was high quality and goalkeeper Angus Gunn did well to tip it onto the underside of the crossbar.
Gunn recovered to grab the loose ball and was barged on the line by Pedro, with referee Andy Davies then indicating he had received a signal to say the ball had crossed the line.
He awarded the goal, to Stoke's fury, and tempers flared on the touchline as fourth official James Linington was consulted.
Had the ball crossed the line from Cleverley's shot? TV replays were inconclusive. Had Gunn taken it over himself? If so, had Pedro's challenge been legal?
There were more questions than answers but the goal stood.
Stoke were unsettled and Gunn immediately had to stop Sarr firing Watford ahead, although the Senegal striker's dithering helped the on-loan Southampton man get into position to block.
Sarr began the second half intent on making amends but a one-two in the Stoke box with Cleverley saw Gunn slide out to grab before Fletcher headed a good chance wide at the other end.
Stoke felt justice was partially served when Powell lashed in an 81st-minute equaliser with a low drive beyond Ben Foster's reach from just inside the box.
But Sarr struck three minutes into added time after Ken Sema had wriggled free on the left and laid the ball back.