Goals from Marc Bola, Edo Kayembe and Edoardo Bove proved enough for the Hornets after Max Cleworth had pulled one back for the visitors.
Wrexham booked a place in the last 16 of the FA Cup for the first time in 29 years thanks to a 1-0 win over Ipswich Town.
Watford keep their Championship play-off hopes alive while denting those of Wrexham by beating the Red Dragons at Vicarage Road.
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Chelsea survive Wrexham scare to reach FA Cup quarters
Chelsea survived a scare as they twice came from behind to beat Wrexham 4-2 after extra time and reach the FA Cup quarter-finals.
Can second-tier upstarts Wrexham beat Premier League giants Chelsea?
Chelsea come from behind twice to scupper 10-man Wrexham's hopes of a giant-killing in a thrilling FA Cup fifth-round tie.
Saints had goalkeeper Daniel Peretz to thank for the three points and a 13th game without defeat.
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