They got the breakthrough when Rangers failed to clear an Anthony McNamee cross and Matthew Spring headed home.
Spring returned the compliment to unselfishly feed McNamee to finish for the second before Young's cross-shot found the net with 15 minutes left.
Dan Shittu headed home Lee Cook's cross in the dying seconds but it was merely a consolation for a poor QPR.
Watford manager Adirian Boothroyd:
"Three points is great but I'm a bit disappointed with the goal at the end.
"We've got to make sure we keep clean sheets because goal difference may be the difference between perhaps reaching the higher echelons.
"We must not get excited - we're not even half-way through the season yet."
QPR manager Ian Holloway:
"We were expecting a better performance than that and we found it very difficult.
"The team I started with was not the team I wanted to pick. Two people had fitness tests (Lee Cook and Marc Nygaard) earlier.
"But the physio and I felt they were not right to play the full 90 minutes."
Watford: Foster, Doyley, Carlisle, DeMerit, Chambers, Devlin, Mahon, Spring (Bangura 83), McNamee, King, Young.
Subs Not Used: Chamberlain, Stewart, Mackay, Henderson.
Goals: Spring 39, McNamee 70, Young 76.
QPR: Royce, Bignot, Evatt, Shittu, Doherty, Dyer, Santos (Nygaard 45), Ainsworth (Cook 45), Gallen, Moore (Langley 74), Sturridge.
Subs Not Used: Milanese, Cole.
Goals: Shittu 90.
Ref: M Atkinson (W Yorkshire).