Lewis McGugan created Watford's first chance of the game as he picked up the ball outside of the box, leaving him with time and space to test the City goalkeeper from range.
Sam Baldock was wasteful for Bristol as he was unable to convert a header that flew high and wide of goal, before McGugan lashed another effort towards the net.
Troy Deeney was next in line for the hosts when he tried to head his effort on target, which edged wide to the keeper's left.
McGugan was involved in Watford's opener as he provided the assist for Marco Davide Faraoni, who crashed an effort into the top-left corner of the City goal.
McGugan looked dangerous after the break and he soon turned from provider to scorer when he grabbed a goal with his left from the centre of the box to put Watford 2-0 ahead.