The Clarets deservedly went in front just before the break through Jay Rodriguez and looked in control when Nyron Nosworthy headed into his own net five minutes after half-time.
Nosworthy quickly made up for his mistake by pulling a goal back with a downward header, before substitute Alex Kacaniklic equalised and Troy Deeney sealed a stunning fightback with 15 minutes remaining.
Burnley were unable to find a way back and slipped to a third consecutive defeat which left them eight points adrift of the play-off places.
With six minutes gone Watford had a golden chance to take the lead when Ben Mee's poor backpass sent Deeney clear but Burnley goalkeeper Lee Grant made a smart block on the edge of the box.
The visitors began to take control and Ross Wallace's cross found Dean Marney who headed over.
Minutes later the Clarets worked the ball to Wallace just outside the box and with no Watford player to close him down he fired in a dipping shot that went just over the bar.
At the other end Lee Hodson evaded two challenges and laid the ball off for Prince Buaben who took a touch before firing in a shot which was tipped over by Grant.
Just as Watford began to get a foothold in the game, they went behind four minutes before the break.
Adrian Mariappa attempted to head the ball back to Tomasz Kuszczak but Rodriguez nipped in and drilled a shot into the corner.
Watford boss Sean Dyche would have wanted to see a reaction from his side after the break but within five minutes of the restart they were 2-0 down.
Wallace sent in a free-kick from the right touchline and the unfortunate Nosworthy headed into his own net.
Four minutes later Nosworthy went some way to atoning for his mistake when he met Sean Murray's corner at the back post and headed in to halve the deficit.
That was Nosworthy's first goal for over eight years and he almost had another moments later when he fired in a first-time shot after a punch from Grant but the Burnley keeper saved with his feet.
Watford drew level with 18 minutes remaining when Joe Garner flicked the ball into the path of Kacaniklic who drove a shot across Grant and into the far corner.
Vicarage Road erupted and the Watford fans were still celebrating when Burnley failed to clear Murray's corner and the ball fell to Deeney who converted from close range.
Burnley pressed for an equaliser and Kuszczak made a superb save low to his left to keep out a half-volley from Rodriguez as Watford held on for the win.