The result continues Rangers' recent improvement under Italian boss Luigi De Canio, although they had to recover from a shaky start to eventually leave Wednesday hanging on for a point.
Rangers looked like the away team in the opening quarter-of-an-hour, such was the Owls' dominance.
Wednesday striker Akpo Sodje headed Yoann Folly's seventh-minute corner against the bar and later shot straight at keeper Lee Camp after leaving defender Bob Malcolm trailing in his wake to latch onto Frankie Simek's long ball.
De Canio's side gradually found a way into the game and Rowan Vine threaded a clever pass through for QPR's on-loan Chelsea winger Scott Sinclair, who was denied by keeper Lee Grant's block.
Vine found the net after being picked out by Martin Rowlands' pass but the effort was ruled out for offside, before Grant tipped Vine's 20-yard drive over the bar.
That brought Rangers to life and they hit the woodwork twice within the space of two minutes near the end of the first half.
First, Sinclair jinked his way past Simek and shot against the outside of the post before Mikele Leigertwood headed Rowlands' corner onto the bar.
The bar was rattled again on the hour mark, this time by Wednesday's Burton O'Brien, whose left-footed curler looked destined for the net.
Sinclair missed Rangers' best two chances of the second half. He fired straight at Grant after being found by Chris Barker's cross and, in a counter-attack following a Wednesday corner, Sinclair ran half the length of the field only to lift his shot over.
Wednesday went close to grabbing a winner when Marcus Tudgay fired into the side-netting late on and QPR playmaker Akos Buzsaky sent a last-minute free-kick just over.