The gift came after 33 minutes when Watford's Micah Hyde handled Mark Wilson's corner and the ref pointed to the spot.
Dutchman Peter Hoekstra beat Alec Chamberlain, drilling the spot-kick to the keeper's right with what was Stoke's first goal attempt.
Watford Boss Ray Lewington insisted his players do not have one eye on the forthcoming FA Cup semi-final and they battled well.
Given that, they had not scored in four league outings and were taking on a side that had recorded four successive clean sheets.
The expected second-half revival was halted when Stoke increased their lead with their second goal attempt of the afternoon.
Hoekstra had already signaled to the bench that he was having problems with a twisted neck. After he had received the ball 25 yards out with his back to goal it was the turn of the Watford defenders to twist their necks as the Dutchman pivoted and hooked the ball into the far corner with an unstoppable shot.
Watford were all at sea but rallied. Tommy Smith had a header tipped over and after flooding the visitors goalmouth with a succession of crosses, they finally broke through after 66 minutes.
Stephen Glass provided a cross and leading scorer Heidar Helguson climbed high to head in his 12th goal of the season.
Despite the ref adding six minutes injury time, mostly for timewasting by the Stoke keeper Mark Crossley, City held on to this their first away win since September.
"We have climbed out of the bottom three before only to slip back in.
"We've had a run of away games and picked up five points from our last three. Now we need to build on that at home," said City boss Tony Pulis.