Deeney then turned provider, setting through Ismaila Sarr to rifle home from an acute angle.
Substitute Steven Fletcher pulled a goal back with seven minutes remaining, but Watford held on to secure a third win in seven days and leave Stoke with just one victory in their last 10 league matches.
Victory was also Watford's first success at Stoke since October 2015 and only their third away league win of the season.
Deeney's sixth goal of the season was his 139th for Watford, edging him closer to the all-time club record of 186 held by Luther Blissett.
Stoke boss Michael O'Neill made four changes to his side which drew at Rotherham, with Tottenham loanee Jack Clarke handed his first home City start, while James Chester, Sam Clucas and James McClean all returned.
John Obi Mikel saw his powerful right-foot shot deflected over the crossbar and the hosts went close again in the 20th minute when Clarke had an effort deflected wide.
Winger Clucas had a shot blocked but the visitors had a decent penalty shout turned down after Adam Masina went down in the Stoke box after a strong challenge from Chester.
And moments later keeper Bursik produced a smart save to palm Chalobah's stinging drive over the bar.
At the other end Clucas volleyed narrowly over from McClean's whipped in free-kick from the left flank.
Wales international Joe Allen dragged an effort across the face of goal and Clucas was within a whisker of poking home from point-blank range.
Watford keeper Daniel Bachmann thwarted Allen with a fantastic reaction save as Stoke nearly broke the deadlock immediately after the restart.
Bursik produced a fine brave save to deny Sarr, but then turned villain when he hauled down Pedro chasing down the rebound.
Deeney stepped up and left Bursik no chance with a powerful strike which would have taken some stopping.
And just five minutes later Sarr latched on to Deeney's pass and picked out the bottom left corner with a fine strike for his fifth league goal of the season.
Clarke had a powerful long-range shot saved by Bachmann before substitute Fletcher pounced to poke home in the box, but despite six minutes of added time Stoke could not grab an equaliser.