© Getty Images
Stoke were equal to the early pressure and staged an attack of their own on the counter in the seventh minute, a move that ended with Charlie Adam firing wide.
The Potters continued to press Norwich, but were restricted to long-range efforts for the most part, including a 30-yard screamer from Adam that flew over the bar in the 27th minute.
Watford were left wondering how the deadlock was still intact in the 38th minute as they struck the crossbar twice in rapid succession, first through Ikechi Anya, and then Deeney on the follow-up.
However, Deeney's lengthy wait for a Premier League goal came to an end two minutes before half time as he collected a pass from strike partner Odion Ighalo and lashed one beyond Jack Butland to open the scoring.
© Getty Images
Stoke went in search of an equaliser in the opening stages of the second half as Shaqiri found himself in space and let fly, putting his effort narrowly over the bar.
It was a miss the Potters would rue as Watford doubled their lead in the 69th minute through Almen Abdi, who put a powerful strike past Butland after being teed up by Ighalo.
Although Stoke had their fair share of chances, the afternoon belonged to Watford, and they almost had a third in the 72nd minute when Juan Carlos Paredes forced an instinctive save out of Butland.
The win moves Watford above Stoke in the table, with the Hornets sitting in 13th place on 13 points and the Potters just behind them on 12.