Webber was in an offside position when he nodded home after Chris Morgan's header from a free kick had come off the bar. United had earlier been guilty of missing several good chances with forward Rob Hulse hitting the post from three metres.
In a stormy clash, Watford defender Chris Powell was sent off for a second booking in injury time while there was controversy as Watford's ball boys used towels to dry the ball for the home side's throw-ins but not the visitors'.
United manager Neil Warnock complained to the officials and even produced his own towel in the second half.
The Yorkshire club remain in the bottom three on goal difference but are level on 13 points with Blackburn Rovers and Newcastle United. Watford are second bottom with nine points.
There are five Premier League games scheduled for Wednesday including leaders Manchester United at home to Everton and champions Chelsea visiting Bolton Wanderers.
