Webber's close-range header in the 87th minute - 13 minutes after he had come on as a substitute - could prove crucial later in the season as United and Watford fight desperately for survival in the Barclays Premiership.
The result was no more than United deserved as they had created by far the better chances of the game, with Christian Nade and Rob Hulse both hitting the post.
By contrast, Watford missed ill forward Ashley Young desperately, and it is hard to see how they will score enough goals to remain in the top flight.
The Hornets' misery was complete in stoppage time when Chris Powell was sent off for a second bookable offence.
Watford made five changes to their starting XI for tonight's game against, with goalkeeper Ben Foster and forwards Hameur Bouazza and Young all sidelined.
United made two changes, Nade - making his first top-flight start - and Chris Morgan chosen in place of Nick Montgomery and Nicky Law.
Nade looked lively for the visitors during the early stages, giving the home defence plenty to think about with his pace, strength and close control.
But it was Adrian Boothroyd's team who had the first good chance in the eighth minute.
Tommy Smith was given far too much room on the edge of the penalty area to turn and hit a rising shot from 22 yards that Paddy Kenny seemed to tip over - yet a goal-kick was given.
Mahon was booked in the 16th minute for a foul from behind on Nade, who was charging towards goal after Malky Mackay had misjudged a bouncing ball in midfield.
Fortunately for the home side, Alan Quinn's resulting free-kick from 30 yards was well off target.
Three minutes later United wasted another chance when Phil Jagielka's left-wing cross was headed wide by Keith Gillespie, who was distracted by Chris Powell's presence.
But in the 22nd minute Watford came even closer when Kenny spilled Darius Henderson's close-range shot following Smith's left-wing corner and he was grateful that Chris Morgan was there to scramble the ball behind for a corner.
The match was a physical, bruising one, and in the 30th minute United defender Claude Davis hobbled off and was replaced in the centre of defence by Leigh Bromby.
Both teams were painfully lacking in finesse going forward and it was difficult to see how either would score a goal from open play.
The home side were perhaps lucky not to concede a penalty in the 36th minute when Nade sprung the offside trap and latched on to a header from Alan Quinn, only to be flattened by Hornets goalkeeper Richard Lee just after he had stabbed the ball wide of goal.
Referee Martin Atkinson gave a goal-kick, leaving United boss Neil Warnock perplexed on the touchline.
At the start of the second half, Nade outpaced Mackay on the left and cut into the penalty area, but his right-footed finish was poor and went well wide of the right post.
The France Under-21 international came even closer in the 51st minute, when he was desperately unlucky not to give his team the lead.
Nade eluded his marker Jay DeMerit to meet Derek Geary's perfect right-wing cross with his head, but United were dismayed to see the ball bounce back off the right post with Lee beaten.
United were frustrated in the 62nd minute when Jagielka sent Gillespie clear for the Ulsterman to cross for the unmarked Nade, who could only send the ball way over the crossbar from eight yards at the far post.
In a desperate attempt to give his team some potency, Watford boss Boothroyd took off Anthony McNamee, making his first Premiership start, and sent on Dan Shittu - a centre-back - to play alongside Henderson in attack.
In the 76th minute, however, United were again denied by the post, Hulse shooting against it from three yards via a deflection off DeMerit following Mikele Leigertwood's cut-back.
Three minutes from full-time the deadlock was finally broken when Morgan's header was pushed onto the crossbar by Lee, and Webber nodded in the rebound from two yards.
To add insult to injury for Watford, Powell was sent off in stoppage time, collecting his second booking for a foul on Hulse.