Conor Chaplin’s goal consigned unlucky QPR to defeat at Loftus Road.
Ipswich, promoted from League One last season and now unbeaten in 22 league games, scored against the run of play with 15 minutes remaining.
Nathan Broadhead found Chaplin in the box and, after his first shot was blocked by Jack Colback, the striker fired the loose ball beyond keeper Asmir Begovic.
QPR had created several chances – and were desperately unfortunate not to be ahead at half-time.
They could not have gone closer to scoring when Sinclair Armstrong’s strike from near the left-hand edge of the penalty area struck the inside of the far post and then the inside of the opposite post.
The pace and directness of 20-year-old striker Armstrong continued to cause Ipswich major problems after that near miss.
Armstrong chased a long ball from Paul Smyth and forced a mistake from the worried Luke Woolfenden before unleashing a shot which keeper Vaclav Hladky did well to save.
Hladky also pushed over Morgan Fox’s looping header from a free-kick swung in by Ilias Chair, who sent one shot narrowly over and another wide of the near post from a tight angle as QPR kept up the pressure.
Ipswich did also threaten before the break. Wes Burns missed a great chance when he was unable to find the target when free at the far post, and George Hirst later fired over from just inside the box.
The visitors were on the back foot again early in the second half – again largely because of the relentless Armstrong.
The young Irishman darted with the ball between Woolfenden and Harry Clarke on the left flank and charged towards the box, where Hladky managed to deny him.
Then an astonishing miss let Ipswich off the hook again.
In trying to add to a decisive touch after good work from Chair, Armstrong inadvertently diverted the ball away from the target towards R’s defender Osman Kakay, who contrived to blast wide of an open goal.
Armstrong, playing in the absence of the injured Lyndon Dykes, is hugely exciting but has shown a lack of stamina so far during his fledgling career.
And when he went off midway through the second half, Rangers inevitably faded and boss Gareth Ainsworth’s limited options were underlined.
Ipswich took advantage and looked comfortable after going ahead, although Chair almost scored a sensational late equaliser when his audacious attempt from near the halfway line was tipped over by the scrambling Hladky.
QPR: Begovic; Kakay, Cook, Fox; Smyth, Field (Dixon-Bonner 67), Dozzell (Duke-McKenna 90), Paal; Willock (Colback 45), Chair; Armstrong (Kolli 65).
Subs not used: Walsh, Gubbins, Larkeche, Richards.