Watford had possession in the first half but struggled to make any inroads against the solid home defence until Etienne Capoue swept a low shot into the net in first half stoppage time.
QPR turned the tables after the break, controlling the midfield but lacking the final touch up front.
Watford, who have never won the competition, put the ball in the net again in the 73rd minute but Andre Gray's effort was ruled offside in a very narrow call.
The visitors did it well in the final minutes, dropping deep to protect their lead as QPR frantically searched for an equaliser and with captain Toni Leistner missing a golden opportunity from point-blank range .
Premier League heavyweights Manchester City are in action on Saturday at Newport County.
(Reporting by Karolos Grohmann, editing by Pritha Sarkar)
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