With Arsene Wenger in the stands, as he served the second of a four-match touch-line ban, the Gunners rallied after a dismal first half, but could not build on Alex Iwobi's effort, as the visitors hung on for a 2-1 win.
The result was Arsenal's first defeat of 2017 and adds even more significance to Saturday's showdown with leaders Chelsea at Stamford Bridge.
Shkodran Mustafi fouled debutant M'Baye Niang and Kaboul's drive from the resulting free-kick took a huge deflection off Aaron Ramsey and flew past Petr Cech.
The second Watford goal followed shortly afterwards, as Etienne Capoue broke forward, eased past Mustafi and, although his effort was saved by Cech, Deeney was on hand to snaffle home the rebound.
Arsenal's goal came from a Alexis Sanchez cross to Iwobi, who netted.
Spurs played out a disappointing goal-less draw with Sunderland away from home and missed an excellent chance to cut the lead on Chelsea.
In other matches, Swansea City beat Southampton 2-1, Middlesbrough drew 1-1 with West Brom, Crystal Palace defeated Bournemouth 2-0 while Burnley beat defending champions Leicester City 1-0.