Alejandro Faurlin had scored his first goal for Rangers, with home manager Neil Warnock, the former Sheffield United chief, attempting to nudge the Owls closer to the drop.
But Soares, who played for Warnock at Crystal Palace, got one over on his former boss with an equaliser 14 minutes from time.
QPR should by then have been home and hosed as they squandered a host of chances, but Wednesday substitute Leon Clarke could have stolen all three points at the death only to shoot straight at Rangers goalkeeper Carl Ikeme.
The first half was all about Faurlin, who was a £3.5million signing of the Flavio Briatore regime back in August - since when the controversial chairman has departed along with four managers.
After a slow start, the Argentinian midfielder looks to have finally found his feet under Warnock and he broke his goal duck in style in the 23rd minute.
Damion Stewart headed a high ball down to the feet of Faurlin, who lashed a half-volley into the back of the net.
Tamas Priskin had already warmed Owls goalkeeper Lee Grant's hands with an angled drive, and he could have doubled the advantage just before the half-hour but lifted his shot over the crossbar.
After the break the Hungarian striker, who is on loan with Rangers from Ipswich, was denied by the fingertips of Grant as he attempted an acrobatic scissor kick.
Grant was well placed to foil Faurlin as the South American looked for a second from 20 yards and Adel Taarabt's long-range effort fizzed over the top.
Wednesday finally gave Ikeme something to do when Tommy Spurr crossed from the left and James O'Connor headed straight into the Rangers keeper's arms.
But the hosts could have doubled their advantage when centre-back Kaspars Gorkss met Taarabt's corner with a powerful header which flew just wide.
Wednesday boss Alan Irvine gambled with 20 minutes left when he sent on Jermaine Johnson, who had just returned from injury, in place of the ineffective Luke Varney.
And the substitution paid off when Johnson fed Spurr and his superb left-wing cross was nodded in by Soares at the far post.
Clarke should have snatched victory for Wednesday from Spurr's late free-kick but he failed to convert the chance in front of goal.