The Reds missed a number of presentable chances against their fellow strugglers, despite playing the final 20 minute with a man advantage.
The Reds probably created the better chances during what was a largely disappointing opening 45 minutes.
Debutant Matt Mills went close early on, firing narrowly over the top after latching on to a knock-down from Kieffer Moore.
Moore was denied by a smart stop from Rangers 'keeper Alex Smithies shortly after.
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The hosts responded with an effort from James Perch, who headed over the top as he roared in to meet Luke Freeman's cross.
The Reds almost broke the deadlock shortly before the break when Adam Hammill's piledriver was brilliantly saved by Smithies.
It was the hosts who finally struck three minutes into the second half.
Former Red Josh Scowen provided the strike, curling home past the outstretched arm of 'keeper Nick Townsend.
The Reds almost replied immediately, with Tom Bradshaw being thwarted by another fine stop from Smithies.
Rangers were then reduced to 10 men in the 71st minute when sub Ryan Manning was sent off for a crude challenge on Mills just four minutes after he had come on.
The Reds couldn't capitalise, though.
Rangers almost made it 2-0 late on, but Conor Washington was denied by a super stop from Reds' 'keeper Nick Townsend.
QPR (4-4-2): Smithies; Perch, Onouha, Lynch, Wszolek; Cousins (Manning, 67), Scowen, Freeman, Robinson; Washington, Smith.
Subs not used: Ingram, Bidwell, Baptiste, Eze, Osayi-Samuel, Oten.
Barnsley (4-4-2): Townsend; Yiadom, Mills, Lindsay, Pinillos (Mahoney, 80); Moncur, Gardner, Williams, Hammill (McBurnie, 68); Bradshaw, Moore (Hedges, 68).
Subs not used: Davies, Thiam, Pearson, Mallan.
Referee: Tony Harrington (Cleveland).