Clarke, just moments after coming on for Danny Graham, sneaked in at the back post to turn a Bakary Sako delivery past a stranded Keiren Westwood with six minutes remaining.
That was enough to seal a morale-boosting 1-0 win for the visitors, who had lost their last five successive Sky Bet Championship matches and were without a win in six.
The hosts began the brighter of the two sides with Stevie May squandering an early chance, the Scotland international rounding ‘keeper Carl Ikeme but seeing Richard Stearman clear his shot off the line.
Wolves reacted well to the Owls’ fast start as midfielder James Henry found space inside the penalty area, however he could only guide Rajiv van La Parra’s cutback over the bar.
That was a rare early opportunity for the visitors, though, and it was Wednesday who continued to dominate proceedings as Royston Drenthe hit a sweet volley from the corner of the area narrowly off target.
The Owls then came within inches of taking the lead as skipper Glenn Loovens mustered a yard in the penalty area, but his header from Chris Maguire’s corner drifted just wide.
May again had the opportunity to break the deadlock midway through the first half at Hillsborough, but after a pinpoint through-ball by Drenthe, he could only bundle the ball into the hands of Ikeme.
Chances were easy to come by in a game that somehow reached half-time goalless with both sides missing gilt-edged opportunities in first-half stoppage time, as Wednesday’s May and Wolves’ Graham both fired one-on-ones wide of the goal.
The second half continued in the same fashion as the first, as after Westwood parried Kevin McDonald’s strike straight to Van La Parra, the Dutchman missed the target with the goal at his mercy.
The midfielder had yet another chance to open the scoring just two minutes later following a clever reverse pass from Henry, but Westwood spread himself well in the Wednesday goal to deny Wanderers again.
Similarly to the first half, the Owls did threaten through striker May, but his best chance after the break was comfortably saved by Ikeme as he created an opening for himself from 15 yards.
The match looked set to finish scoreless but, with just six minutes to play, Clarke came back to haunt his old club as he smashed in Sako’s cross, sending the Midlands club on their way to their first victory in seven games.
Wednesday’s bright spark throughout the game, Maguire, then nearly dragged the hosts level, but his vicious free-kick narrowly missed the target.
Stuart Gray’s side continued to press in search of a stoppage-time equaliser, but despite numerous crosses into the Wanderers’ 18-yard box, they could not find the breakthrough.