Leroy Fer and Bobby Zamora scored first half goals for the west Londoners who won away at the 12th time of asking after chairman Tony Fernandes hinted on Twitter at the appointment of a "dream manager" to replace the departed Harry Redknapp.
"It's a very important result," QPR interim boss Chris Ramsey told Sky Sports. "It's been a long time coming.
"We have had some good away performances but we just haven't had the rub of the green.
"It's nice from a visual point of view to see yourselves above the (relegation) line. We need to stick together and continue to perform like that.
"The goals that we got were great and a good quick fast start was important for us. The boys kept the momentum up throughout the game."
QPR have climbed to 17th but are still embroiled in a fierce relegation battle and only lead Aston Villa, who are now in the drop zone after losing 2-0 at Hull City, on goal difference.
Rangers have been without a manager since Redknapp quit last week to have an operation on his knees and Ramsey said he would be happy to be considered for the job on a permanent basis.
"The club's been really good to me and I was really focussed on the job at hand and whatever's going to happen will happen," he said. "If the job's available and I'm the right man then I'll do it."
(Reporting by Tom Hayward; Editing by Ken Ferris)
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