Neither goalkeeper was called into any demanding action during the opening 45 minutes.
However, the second half got off to a positive start when Watford's Craig Forsyth headed over from close range.
The deadlock was broken on the hour mark courtesy of Ishmael Miller. Goalkeeper Lee Camp's long clearance caused hesitation in the home defence and Miller capitalised to steer the ball beyond Scott Loach.
Miller's replacement, Marcus Tudgay, then forced a low save from Loach as the final whistle neared.
Watford pressed for an equaliser late in the game, but Camp was only called into action on one occasion when he held John Eustace's low effort.
On Tuesday Forest travel to Burnley, while Watford will play host to Millwall.