Glenn Whelan limped off before Owls team-mate Lee Peacock followed four minutes before half-time.
And worse followed for Wednesday, when Drissa Diallo was stretchered off six minutes after the break.
Rangers dominated but Kevin Gallen missed their best chance when he shot straight at goalkeeper David Lucas after being put through by Tom Doherty.
Gallen also missed the target following a cross from Gareth Ainsworth, who himself went close with a spectacular volley which Lucas pushed away at his near post.
Wednesday rallied and substitute Chris Brunt headed wide of keeper Simon Royce's right-hand post.
And it took a last-ditch challenge by defender Matthew Rose to stop Ritchie Partridge after the Wednesday man beat the offside trap.
Wednesday battled on after losing Diallo and after Hills was dismissed for a second yellow card for a crude challenge on Ainsworth.
QPR's veteran striker Paul Furlong twice headed over after being picked out by Marcus Bignot, before Gallen shot over.
Rangers midfielders Doherty and Marc Bircham had efforts saved by Lucas and Bircham saw another shot fly wide.
Rangers manager Ian Holloway replaced Adam Miller with former Aston Villa forward Stefan Moore in an attempt to give his side extra impetus.
But they were unable to break the deadlock and were almost undone at the other end when Royce had to save at the feet of Adam Proudlock after hesitation by centre-back Daniel Shittu.
Royce also had to be alert to keep out a driven shot from Craig Rocastle.
The draw lifted QPR up to fourth in the Championship table and stopped the rot after two straight 3-0 defeats.
But their failure to score for the third game in a row will do little to lift the spirits of their fans following the ousting of popular chairman Bill Power.