Jordan Hugill’s superb goal gave QPR their first points since the season resumed.
The Middlesbrough-born striker lobbed keeper Dejan Stojanovic with a first-time strike from 25 yards after being found by an excellent ball in behind the home defence by Ryan Manning.
It came just after the half-hour mark and was Hugill’s 15th goal of the season.
However, he was injured in the process and limped off with what looked a hamstring problem.
Rangers, beaten in their previous three matches, continued to threaten after the goal and Stojanovic kept out Ilias Chair’s shot and Manning’s free-kick.
Relegation-threatened Middlesbrough, now managed by former QPR boss Neil Warnock, struggled to create clear-cut chances.
Their best opportunity fell to Lukas Nmecha and he blasted over from Jonny Howson’s cross.
It was a fairly comfortable afternoon for keeper Joe Lumley, who was recalled to the Rangers side in place of Liam Kelly.
Subs not used: Kelly, Rangel, Gubbins, Clarke, Shodipo, Bettache, Masterson.