The all-important goal came just before the interval, as Neil Cox powered the ball home from close range, following an initial header by Sean Dyche.
Before that point the game had been fairly even, with few clear chances for either side.
After the setback, Forest went looking for an equaliser, with Jim Brennan prominent on the left side for the home side, but loan star Danny Webber almost doubled the Hornets' lead, bringing a fine save from Darren Ward.
Ward had to be alert to make a fine stop from Tommy Smith, after David Johnson's long-range effort had brought a rare save from visiting keeper Alec Chamberlain.
However, the highlights of the second half were the two red cards in three minutes.
Prutton was dismissed for a late lunge on Allan Nielsen and Lester followed soon after for an equally poor challenge on Neal Ardley.
Some Forest fans came on to the pitch after the second red card, but were soon led off and they were left with nothing to show for the day as the visitors held out for all three points