A goal from Etienne Capoue proved to be the difference as Watford claimed their third triumph in four games, while Swansea remain in the bottom three after failing to find the breakthrough at Vicarage Road.
The visitors had another chance before the quarter-hour mark after Gomes failed to deal with a cross, but Federico Fernandez missed with a header from close range.
Both teams were threatening inside the final third, but the next clear chance came through a Niang free kick, although he was again denied by Fabianski.
In what was proving to be an entertaining tussle, Swansea tried to respond through Sigurdsson but his shot lacked the power to trouble Gomes.
However, Watford edged in front with three minutes of the first half remaining as Capoue claimed his sixth goal of the season on the rebound after initially seeing a shot saved by Fabianski.
Soon after the restart, Sigurdsson got a strike away to signal Swansea's intent for the second half, but Watford were delivering another solid performance under Mazzarri and Janmaat almost made it two with a powerful effort from distance.
Abdoulaye Doucoure - via a deflection from Deeney - went close as well as the home team looked to put distance between themselves and their opponents but as the game approached a conclusion, Sigurdsson was only denied a leveller from a free kick by a good save from Gomes.
Soon after four minutes of added-on time were signalled by the fourth official, Swansea could have equalised through a header from Sigurdsson but after that went wide, Watford were able to celebrate a hard-fought success.