QPR recovered from an early setback to rubber stamp their credentials as top six candidates.
After just three minutes Kevin Gallen reached for a Lee Cook cross but the ball was always going away and the header flashed wide.
Then Rangers were rocked on their heels when an innocuous centre from Martin Devaney was allowed to drift past everybody and into the far corner.
Cheltenham have led 13 times this season and still not got a result and so it was to be that they did not win this one either.
On 15 minutes the Robins goal led a charmed life as first Marc Bircham had a shot cleared off the line. Richard Langley's corner was punched out inches under the crossbar and the same player had his second effort scrambled away.
Bircham's spectacular overhead effort smacked the top of the crossbar on 18 minutes and Paul Furlong's angled header tested Shane Higgs before the Cook-Gallen axis struck.
The on-loan winger weaved past three defenders before crossing to Gallen who hooked home first time to leave the keeper rooted to the spot - there was little Higgs could do about Rangers' second either.
Langley's measured ball seemed odds on to find Gallen but Mike Duff got their first only to clip it into his own net.
The hapless defender knew it was not his night when he became the second stretcher victim following Tom Williams after Duff clashed heads with Furlong in the second half.
In the second half it was all QPR and no surprise when the outstanding Cook raced onto a Langley centre to slide home from point blank range.
Langley was again the provider when Furlong took the ball on the edge of the box with his right foot, swivelled and fired with his left to leave Higgs a forlorn figure.