Deeney converted a 64th-minute penalty after Potters keeper Josef Bursik fouled Joao Pedro.
The veteran striker also provided the assist for Ismaila Sarr to double Watford's advantage from an acute angle.
Stoke substitute Steven Fletcher got one back with seven minutes left to play.
But Watford kept its composure to seal a third successive win, leaving Stoke with just one victory in its past 10 league matches.
Watford's third away league win this season lifted it level on points with second placed Swansea City, which is ahead on goal difference as the race for promotion to the Premier League hots up.
Deeney's sixth goal of the season was his 139th for Watford, edging him closer to the all-time Hornets record of 186 held by Luther Blissett.