Watford's Etienne Capoue smashed a swerving shot past keeper Thibaut Courtois and into the top corner of the net after 55 minutes following a cross from the right by Adlene Guedioura.
Chelsea equalised 10 minutes from time, substitute Michy Batshuayi following up to tap the ball home for his first goal for the club after Eden Hazard's fierce shot was saved by Heurelho Gomes.
Substitute Cesc Fabregas then released Diego Costa with a sublime pass and the striker finished calmly three minutes from the end to seal victory for Antonio Conte's team.
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(Reporting by Ed Osmond; Editing by Tony Jimenez)
