The visitors, who had not won away from Vicarage Road in the league this season, got off to the best possible start when a mistake by Clarke Carlisle was seized upon by striker Will Hoskins, who raced clear of the Burnley defence and threaded a shot through the legs of goalkeeper Brian Jensen.
Hoskins was denied a second as he slipped a shot across Jensen only for Carlisle to head the ball behind for a corner.
Burnley equalised on 24 minutes from the penalty spot after central defender Leigh Bromby handled a cross from Wade Elliott. The penalty kick was converted into the top corner by Graham Alexander for the midfielder's fourth league goal of the season.
Watford went in front for the second time on the stroke of half-time when John-Joe O'Toole found Lee Williamson and his cross was turned in at the far post by a grateful Hoskins.
But Watford's lead lasted only moments when inside the opening minute of the second period a cross from Elliott found Martin Paterson, who shot on the turn beyond Richard Lee to square things at 2-2.
Watford were almost back in front immediately as O'Toole volleyed just over the crossbar, while at the other end from an Elliott corner Carlisle headed inches over the crossbar.
The winning goal arrived on 69 minutes as substitute Chris Eagles sent man of the match Chris McCann to the byline, from where the midfielder delivered a fantastic cross for Elliott to score with a rare headed goal.
Hoskins did have a chance to equalise, but put a free header from a corner wide late on.