It was heartbreaking for the Owls, who had played with more passion and coherence throughout and they are now left in even more trouble at the foot of the table.
Right from the kick-off, it appeared evident that both teams were up for the battle. It was end-to-end stuff in the first 10 minutes, though neither keeper was overly troubled. A long-range effort from Owls captain Glenn Whelan went a few yards wide in the fourth minute.
On the quarter hour mark, a diving header from Sam Collins went a yard wide of Wednesday's goal, but there was not much else to split the two sides.
David Graham's 20-yard shot in the 21st minute was the Owls' closest effort of the half, as he turned well on the right wing to fire just over. A minute later, Wednesday's first corner of the game was safely collected by Boaz Myhill.
But as the half wore on, the floodlights kicked in and the temperature began to plummet, there was nothing of any real note to warm up either set of fans and the initial urgency was largely dissipated.
Wednesday began the second half with much more purpose, no doubt boosted by their ever-vocal fans they were now playing towards.
There was a rare lifting of the atmosphere among the home crowd in the 55th minute when Tigers captain Nick Barmby stepped up to take a free-kick just outside the area on the right, but it was disappointingly long and missed all of City's danger men.
In what proved to be a match-changing tactical move, Peter Taylor threw on Price for defender Mark Lynch in the 60th minute. But seconds later, a powerful left-footed shot from the Owls' Daryl Murphy went a few yards wide.
Three minutes later, a dangerous cross from the byline by Murphy put Myhill under pressure. In response, Taylor introduced last year's top scorer Stuart Elliott to bolster the attack.
Clever work by Price won City their first corner in the 69th minute, which was a telling statistic. Leon Cort could not convert, however, heading over.
It was still Wednesday who looked more threatening and in the 77th minute Cort had to pull off the challenge of the match to deny Steve Adams just yards out with Myhill beaten.
With barely four minutes left, most people in the ground thought Elliott had scored with a cracking header, but it was ruled offside.
There was nothing wrong with Price's 87th-minute matchwinner though and despite a last-ditch effort from Graham Coughlan, who while lying on the floor about six yards out, poked a leg out and shot inches wide, it was Wednesday who went home with the relegation worries.