Goals from David Norris and Daryl Murphy barely began to reflect how dominant the visitors were in the opening 45 minutes.
But Mick Harford's hosts improved after the break, with Jay Simpson pulling a goal back from close range.
Yet they could not find an equaliser and are now just two points off the relegation zone, having taken one point from their last six games.
That is one point above Ipswich, but the Tractor Boys are in form and look more likely to escape the drop.
QPR haven't kept a clean sheet since they beat Preston way back in October - and since then they've already got through two permanent and two caretaker managers.
And their terrible defensive record continued after just eight minutes when Norris was given all the time in the world to pick his spot past Carl Ikeme from 16 yards, although the ball did deflect in off Kaspars Gorkss.
It should have been two after just 20 minutes with Ikeme somehow keeping out Norris' close-range header before getting up to bravely deny Pablo Counago.
Murphy was he next man to miss a gilt-edged chance, somehow slotting wide of goal after Jon Walters' superb back-heel had found him in space on the edge of the six-yard box with the goal gaping.
But the on-loan Sunderland striker made amends with seven minutes before half-time as he doubled Ipswich's lead.
Norris was the creator this time, cutting in from the wing and laying the ball off to Murphy, who was again given all the time he needed to score from inside the box for his second goal in two games.
Flavio Briatore, QPR's co-owner, was roundly booed as he left his seat at half-time and the Italian failed to retake his seat for the second half.
But if he had stayed he would have seen an improved display by his side, although they couldn't have got any worse.
Simpson hauled them back into the contest when he lashed home when the ball fell kindly to him in the six-yard box.
But despite constant pressure they couldn't grab a second and must be seriously worried about whether they will be in League One next season.