The opening 10 minutes of the game were a scrappy affair, with both sides giving away a number of fouls.
Fernando Forestieri had the first real chance of the game on 12 minutes, but after a neat piece of skill his shot was blocked for a corner.
Watford were doing most of the pressing but were struggling to find a way through the hosts' defence.
Alexandre Geijo had a chance with a snapshot after a Forestieri cutback, but was unable to find the target.
It was the struggling Bristol who opened the scoring with two minutes remaining in the first half, Almunia misjudging a Greg Cunningham cross and seeing the ball go in off the post.
Watford came forward in search of the equaliser but in the 65th minute fell further behind.
Watford again came forward, dominating the possession, but City remained strong to claim a crucial three points.