The visitors were composed throughout the 90 minutes and Mark Hughes' team were much the more industrious, while Watford offered little in terms of resistance.
Still, Stoke had good fortune to thank as Charlie Adam's header cannoned off the Watford goalkeeper and back into his own net just before the half hour mark.
The warning signs were there early for Watford, with Gomes having to be alert to deny a point-blank shot from Bruno Martins Indi on seven minutes after Watford failed to deal with Xherdan Shaqiri's free kick into the box.
At the other end, Daryl Janmaat took advantage of a weak cross field pass to gallop forward and test Lee Grant with a low shot from 25-yards.
On the quarter hour, the impressive Giannelli Imbula fizzed a left-foot shot inches wide of the Watford post with Gomes flailing.
Frustration began to grow for the Hornets when Younes Kaboul limped off injured before 20 minutes had elapsed, with replacement Christian Kabasele taking several minutes to ready himself for action.
The home side then found themselves behind when Shaqiri's corner was met by the unchallenged Adam, who headed against the woodwork. The ball rebounded off the static Gomes and over the line.
Odion Ighalo was sent on after half time but Watford rarely looked like restoring parity. There was a moment's concern for Stoke with 15 minutes left when Erik Pieters tested Grant's reactions with a looping header backwards that threatened to end up in his own net.
Shaqiri blasted a free kick into the wall for Stoke, while Janmaat volleyed over the crossbar after collecting a weak header from Martins Indi.
Watford skipper Troy Deeney had the last half chance but he couldn't direct Janmaat's looping cross on target.
The misery for the home side was compounded in stoppage time when Miguel Britos was sent off for a second bookable offence.