The 22-year-old latched onto a Neal Ardley through-ball and rounded Chris Day to fire in on 12 minutes.
He turned well but blasted over moments later but Bruce Dyer stooped to head home on the stroke of half-time.
Webber broke clear and fired in after hitting the post and Rangers will rue having a Kevin McLeod effort ruled out for a challenge on the goalkeeper.
QPR boss Ian Holloway was unhappy that the referee disallowed a goal for Rangers:
"We needed a decision there and it might have settled us down," he said. "It was an absolutely crazy decision. Some of the Watford people around me in the stands were laughing, it was so blatant, and one of their goals was offside!
"But I didn't expect my team to defend like that. We were hesitant and got caught cold. After the heat of Saturday I thought some of my lads looked dead on
Watford: Lee, Chambers, Cox, Dyche, Mayo, Devlin, Gunnarsson,
Mahon, Ardley (Young 79), Webber (Bouazza 89),
Dyer (Helguson 65).
Subs Not Used: Chamberlain, Darlington.
Booked: Mahon, Cox.
Goals: Webber 12, Dyer 45, Webber 59.
QPR: Day, Bignot, Gnohere, Santos (Furlong 46), Padula,
Rowlands (Cook 63), Johnson, Rose, McLeod (Bean 46), Thorpe,
Subs Not Used: Ainsworth, Cole.
Booked: McLeod, Rowlands.
Ref: A Bates (Staffordshire).