The on-loan Manchester United winger took advantage of Carl Hoefkens' sloppy defending to score the winner from 12 yards after 54 minutes.
Stoke nearly levelled but keeper Ben Foster - on loan at Watford after being signed by Manchester United from Stoke - saved brilliantly from Luke Chadwick.
Eagles wasted a great chance three minutes from time, prodding over the bar after Hameur Bouazza's cross.
Stoke boss Johan Boskamp after his coach Gerry Taggart was sent from the dug-out for allegedly using abusive language to the fourth official:
"He grabbed Gerry by the arm, and then Gerry said something to him. Can you imagine what would have happened if Gerry grabbed the linesman?
"Yes, he strayed outside the technical area, but sending him to the stands was not correct."
Watford: Foster, Doyley, Mackay, DeMerit, Stewart, Eagles, Mahon, Spring, McNamee (Bangura 70), King, Henderson (Bouazza 81).
Subs Not Used: Chamberlain, Chambers, Mariappa.
Goals: Eagles 54.
Stoke: Simonsen, Hoefkens, Broomes, Duberry, Brammer, Harper (Dyer 78), Junior, Chadwick, Henry, Gallagher, Sidibe.
Subs Not Used: Sweeney, Kopteff, Dickinson, Duggan.
Ref: P Crossley (Kent).