The away side broke the deadlock early courtesy of Charlie Austin, who rippled the middle of the net with a low shot from six yards out.
Following Burnley's strong start, Watford replied with an equaliser through Troy Deeney, who hammered the ball into the bottom-right corner of the net with a 25-yard shot following impressive build-up play from the home side.
Despite levelling the scoreline, Watford were dealt a blow when Alex Kacaniklic was brought down in the area to win a penalty for the visiting team.
Burnley's goalscorer Austin stepped up to take it and hammered the ball into the middle of the net to give his side the lead.
Watford, who can leapfrog Hull City in second place with a victory on home turf, replied to their deficit by drawing level on 2-2 due to a strike from Fernando Forestieri.
The Argentine slipped into the penalty box after picking up the ball from Fitz Hall to slide it into the back of the net to leave the first half all square.