John Terry scored the first goal on an evening of celebration.
Terry, who is leaving this season after 22 years with the club, hooked home a loose ball from a Willian corner in the 22nd minute.
The defender has scored in 17 consecutive Premier League seasons.
But the former England captain was at fault for the equaliser when barely two minutes later he back-headed a ball he should have cleared, sending it straight to Etienne Capoue for an easy headed goal.
Another defender, Spain's Cesar Azpilicueta, put Chelsea ahead in the 36th minute and striker Michy Batshuayi scored Chelsea's third goal four minutes into the second half.
Watford put a brief damper on fans' celebrations of the title won last Friday, with Daryl Janmaat dribbling through for Watford's second goal and substitute Stefano Okaka equalising against the makeshift Chelsea side in the 74th but Cesc Fabregas scored the winner in the 88th minute.
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