Tom Cleverley scored the match winner just before half-time as the Hornets saw out the final ten minutes despite being down a man.
The result sees the hosts reach the summit of the table on nine points, unbeaten in their opening three matches.
Story of the match
The Clarets had an early shout for a penalty as Hassane Kamara brought down Benson and despite the protests of Kompany, referee Thomas Bramall waved play on.
Choudhury had the first opening of the match, sending a shot on goal, but not causing any meaningful damage. He was frequently bossing play for the hosts, starting or breaking up play.
Arijanet Muric nearly cost Burnley on nine minutes as his hurried pass out of goal was intercepted by Ismalia Sarr, but he couldn't capitalize on the chance.
Despite Choudhury winning the ball high up in the visitors end, which resulted in sustained possession, Watford were unable to create anything of substance.
The Clarets were able to play their possession-based game to gain a foothold in the contest with halftime quickly approaching.
Before the interval, the Hornets went in front in the first minute of stoppage time. Excellent interplay between Sarr and Ken Sema on the right side of the box resulted in a sliding Cleverley finishing past Muric into the bottom corner.
During the goal, Cleverley was injured and unable to continue, replaced by Dan Gosling. Cork came on for Dara Costelloe for Burnley.
Samuel Bastien then sailed his shot over the crossbar from just inside the box.
The hosts then had several set-pieces, but couldn't break down a determined Burnley defenxe. Sarr was replaced by Vakoun Bayo. Yaser Asprilla also came on for Joao Pedro as the duo were making their competitive debuts.
Maatsen sent a cross to Brownhill at the near post, but Bachman was on hand to deny the midfielder's volley with 20 minutes remaining.
In the final ten minutes, the Hornets were reduced to ten men as Kamara failed to properly control a back pass to Bachmann and that resulted in him bringing down Vitinho.
Following the dismissal, Edwards brought on Christian Kabasele and from the resulting free-kick, Bachmann stopped Brownhill for a third time on the evening.
After another fine stop, Ian Maatsen hit the post with the rebound and moments later, Brownhill struck the crossbar.
Player of the match: Daniel Bachmann
Made several outstanding saves, particularly on Brownhill, frustrating Burnley at every opportunity.
The Watford goalkeeper has already kept two clean sheets in the Hornets first three matches to anchor a stingy defence.