Defeat at Vicarage Road left Sunderland seven points from safety, with just nine league games remaining.
The northeast side had kept the game goalless for nearly an hour when Uruguay defender Britos broke the deadlock in the 59th minute.
After the ball had bounced around the box and hit the crossbar, a leaping Britos headed the ball down and into the goal to the delight of the home crowd.
But his lone resistance could not prevent Watford recording their first win in five matches, a result that put daylight between the Hornets and the relegation zone.
By contrast, Sunderland have not even scored in their last five games and even the return of Jermain Defoe, on target for England in their 2-0 win over Lithuania in a World Cup qualifier, could not stop the rot.
Pickford was tested early on, palming a Niang shot to safety before producing a brilliant diving save to turn Doucoure's follow-up over the crossbar.
Stefano Okaka missed a glorious chance to put Watford in front but his free header sailed over the crossbar, before Etienne Capoue curled a shot wide.
Watford lost the experienced Younes Kaboul to a hamstring injury shortly before the break.
Pickford made another good save to deny Niang again and, from the ensuing corner, Craig Cathcart headed straight at the Black Cats keeper.
The deadlock was finally broken just before the hour mark with a scrappy goal.
Okaka met Tom Cleverley's corner with a header which Sunderland forward Fabio Borini unintentionally headed onto his own crossbar.
The ball came out to Cathcart, who headed it across goal for Britos to score at the far post.
Pickford then made another good save, with his legs, when left one-on-one with Watford substitute Isaac Success but was beaten by a Jose Holebas shot that just cleared the crossbar,
One goal, however, proved enough for Watford.