Hornets defender Dale Bennett put through his own net to give Eddie Howe's side the lead but Danny Graham found the net to equalise.
But the visitors were much-improved after the break and goals from man of the match Chris Eagles and former Scotland striker Chris Iwelumo wrapped up the win.
Malky Mackay's side have lost momentum in recent weeks but the victory leaves Howe's men just outside the play-off places.
Watford were fast out of the blocks and should have scored after just 17 seconds.
Graham turned a ball on for on-loan Manchester United midfielder Daniel Drinkwater who was somehow allowed to burst clear on goal.
He only had Clarets goalkeeper Lee Grant to beat but crumbled and sent his shot wide from just inside the penalty area.
It was a huge let-off for the visitors and they took full advantage to take an eighth-minute lead in crazy circumstances through their first real attack.
A through-ball at the end of a decent move was slightly overhit and goalkeeper Scott Loach raced out to clear as Jay Rodriguez chased it down.
Loach got there first but smashed his clearance into the back of Bennett who could only watch as the ball flew backwards into his own net.
However, to Watford's credit they were level in just five minutes.
Marvin Sordell pulled off into space on the right and delivered a cross to the near post where Graham got ahead of his marker to beat Grant with a low first-time finish.
It was the former Middlesbrough man's 19th goal of a prolific season, and he nearly returned the compliment to Sordell moments later but he was unable to beat Grant from 20 yards.
A cracking first half then saw the visitors come close. Rodriguez did well to beat his man on the right flank and picked out Eagles with a gem of a pass but the former Manchester United man shot straight at Loach.
Howe's men should have scored after the break.
Eagles showed quick feet to beat Lee Hodson and send in a fine cross which Rodriguez should have converted but the new England Under-21 cap volleyed wide.
Eagles - who enjoyed a loan spell at Vicarage Road earlier in his career - was the instrumental figure of the second half and deservedly put Burnley ahead in the 66th minute.
The winger played a lovely one-two with Iwelumo to burst into the area and kept his cool to clip the ball under Loach and into the net.
And Iwelumo profited from Eagles' industry in the 75th minute with a powerful back-post header after Eagles had again beat his man to stand up a cross.
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