Goals from Jordan Rhodes, Gaston Ramirez and Ben Gibson gave Boro the points at Loftus Road, with a fine Jamie Mackie strike having brought mid-table QPR level at 1-1 by halftime, before the hosts forced a tense finish with a Tjaronn Chery effort.
The victory takes the visitors to 73 points and within two of leaders Burnley who visit Brighton & Hove Albion, now down to third place with 71 points, on Saturday.
Rhodes opened the scoring after 17 minutes by taking advantage of a mistake from Grant Hall, who misjudged a long through ball, and rounded keeper Alex Smithies before netting.
Mackie equalised just past the half-hour mark with a brilliant shot on the turn that hit the bar and bounced down over the line with the linesman giving the goal.
Boro went back in front six minutes into the second half when Ramirez flicked home a header from a corner swung in by Grant Leadbitter, who had just had a penalty saved.
Gibson's powerful header five minutes later gave Boro some breathing space until Chery's fine left-foot strike from outside the area in the 85th minute set up an exciting finale.
(Writing by Ken Ferris; Editing by Pritha Sarkar)
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