Strike duo Alan Lee and Jon Walters were both on target for Town before sub Paul Furlong's second-half effort ensured a nervy final 20 minutes.
Town had gone six games without a goal before this match to plunge to the fringes of the relegation zone, but victory here, coupled with results for the other strugglers give them crucial breathing space.
QPR came out of the blocks superbly and could have scored twice in the first four minutes as first Lewis Price fumbled a Lee Cook free-kick behind for a corner and then Cook's cross was glanced narrowly wide by Ray Jones.
In between those efforts, Rangers had a good shout for a penalty when a Cook corner was hooked goalwards by Gareth Ainsworth and appeared to strike the raised arms of an Ipswich defender, but referee Rob Lewis said no.
Ipswich created their first chance on ten minutes and should have scored from it as Lee's lay-off set up Gary Roberts, but he showed his lack of a right foot by trying to bend it with his left and fired way over.
Price fielded a low Cook drive with ease before Jaime Peters got the home crowd excited with an angled shot which flashed into the side-netting.
Martin Rowlands curled wide coming in off the right wing before Lee's good run and cross found Roberts, but his pull-back found only visiting defender Sampsa Timoska who cleared.
Walters was denied his first Ipswich goal on 25 minutes when his glancing header from a Roberts free-kick was brilliantly saved by the diving Lee Camp but Town went ahead a minute later.
Roberts, coming back to his best after a poor recent run of form, was the creator with his left-wing cross perfect for Lee to head firmly past Camp for his 13th goal of the season.
Rangers could have been back in it soon afterwards when Cook played in Rowlands who controlled neatly and shot from an angle, but Price dived to hold the effort.
Alex Bruce bravely charged down a goalbound Ainsworth shot before Ipswich finished the half with a flourish which should have brought them a second goal.
Lee blazed over after strike partner Walters chested down for him, Lee then had a goalbound effort deflected over by Damion Stewart and then Camp held a 30-yarder from Walters at full stretch.
Camp made two more good saves early in the second half, scooping away a Jason De Vos downward header from a Roberts free-kick, and then holding an angled Walters effort.
Walters, a £100,000 transfer-window signing from Chester City, netted his first Town goal on 54 minutes to give Ipswich a two-goal cushion, racing onto a Roberts throughball to net through Camp's legs.
Price saved from Rowlands a minute later after Town failed to clear a Cook cross and the outstanding Cook drilled a left-foot drive beyond Price on 62 minutes but Jones had fouled Sylvain Legwinski.
The Frenchman was involved next at the other end with his prod forward seeing Walters spin beyond Stewart but he fired straight at Camp, when perhaps he could have gone round the keeper.
Walters was through again onto a Lee flick, but the angle was tight and although his shot was fierce, Camp beat it away, and it proved a key save as a minute later QPR scored.
Dan Harding backed off to allow Rowlands to fire in an angled effort which cannoned back off the far post and fell perfectly for Furlong to continue his amazing scoring record against Ipswich down the years.
Price immediately saved from Furlong before Camp produced yet another fine save to dive and fist away a 25-yard pile-driver from Owen Garvan.
Both sides made changes as time ticked by, and two of Town's subs combined in a move which could have brought a third two minutes from time as Danny Haynes put in loanee Francis Jeffers and his curling effort was brilliantly palmed away by Camp.
Four minutes were to be added, but in the end nearly six were played, with Rangers having a shout for a penalty when Furlong appeared to be held by David Wright as he chased an Adam Bolder throughball, but Mr Lewis let play go on and Furlong fired over from an angle.
Ipswich just about deserved the points, although Rangers deserve credit for their spirit to make it so tense in the final 20 minutes, but this loss ensures a nervy finale to the season for John Gregory's men.