The striker got across his marker to meet Dwight McNeil's splendid cross at the near post to guide a header past Ben Foster in the 73rd minute.
The result lifted the Clarets into 11th spot in the Premier League and left the Hornets scrapping for their lives at the bottom end of the table.
Here are the player ratings...
9. Jack Cork 7
His work rate and attitude epitomises the culture and philosophy of the club. Never stops running until the final whistle, even with five extra minutes added on. His hard-working nature, and covering play, makes life easier for his team-mates.
10. Jay Rodriguez 8
Could have finished with more than one goal on the night, but the striker deserved to be the match-winner. He tested Foster early on, had another strike cleared off the line by Dawson, but his movement and finish in the 73rd minute was exceptional.
11. Matej Vydra 7
The Czech Republic international has built up a brilliant understanding with Jay Rodriguez. The pair combine well and he was unlucky not to add to his tally. The forward hit the upright in the first half and was then denied by Foster in the second.