Gabrielle Angella, the Italian defender who moved to Vicarage Road from Udinese in the summer, gave Gianfranco Zola's side the lead before Watford were pegged back by Lewis Grabban's equaliser.
Angella and Deeney scored in quick succession to put Watford back in control and the Hornets, who were the leading goalscorers in the division last season, then turned on the style.
Lewis McGugan scored the fourth before Deeney completed his hat-trick with a powerful 20-yard strike into the corner and a last-minute penalty.
Nottingham Forest and Blackpool are the only other teams so far to have opened their Championship campaign with two victories but both left it late to win.
Forest snatched the points against Blackburn with a last-minute strike from Darius Henderson after a mistake from Rovers goalkeeper Jake Kean, while an own-goal from Barnsley's Scott Wiseman sealed a dramatic late victory for Blackpool.
Barnsley's defeat leaves them as one of six teams yet to win a point in the Championship and they are joined down the bottom of the table by Millwall, who were beaten 3-0 by Ipswich.
Mick McCarthy's men took the lead in fortunate fashion with an own-goal from Shane Lowry but they built on that with headers from Tommy Smith and Paul Anderson to seal the win.
Charlton also suffered their second successive league defeat of the season as Middlesbrough, having lost to Leicester and Accrington Stanley, finally tasted victory with a goal from Lukas Jutkiewicz.
Burnley may have lost striker Charlie Austin but they had enough of a goal threat to beat Sheffield Wednesday 2-1, with Danny Ings and Sam Vokes putting them ahead before David Prutton bagged a consolation.
Source: PA
Source: PA