Clarke lashed home the opening goal from 20 yards in the sixth minute and steered home his fifth of the season just after the hour to halt a run of three straight defeats for Wednesday and inflict Leicester's first defeat since January 26.
Owls manager Alan Irvine made four changes to the side thrashed 5-0 at relegation rivals Reading last week, with captain Darren Purse, Jermaine Johnson, Tommy Miller and Clarke all returning to the side, while the Foxes were unchanged from the side which beat Nottingham Forest the previous weekend.
Clarke had already forced Leicester goalkeeper Chris Weale into a fine save with a thumping 20-yard volley inside the first minute before he gave Wednesday a shock early lead.
The big forward, who had only found the net on three prior occasions this season, had clearly got his shooting boots on as he crashed a shot into the top corner from just inside the area.
Weale was then forced to gather Jermaine Johnson's mis-hit effort before Leicester striker Martyn Waghorn's header was easily held by Owls goalkeeper Lee Grant.
Waghorn made a better fist of his next effort on target, unleashing a left-footed volley that Grant turned away at full stretch.
Leicester were dealt a blow in the 30th minute when Weale was forced out of the action through injury and replaced by Conrad Logan, but the switch did not affect the Foxes, who dominated possession until half-time without forcing Grant into further action.
The visitors were indebted to Logan two minutes into the second period when he tipped away another scorching shot from Johnson.
Leicester responded through their main threat Waghorn, who saw his shot held by Grant, but Wednesday increased their advantage soon after.
Johnson, recalled to the side for the first time since mid-January due to a hamstring injury, beat his man out wide and clipped over a fine cross for Clarke, who used his bulk to muscle in and convert from six yards.
Leicester stepped it up a gear and almost reduced the arrears in style through Lloyd Dyer, but the midfielder's scorching drive was brilliantly kept out by Grant, while Wayne Brown headed Waghorn's corner just over the crossbar in the 72nd minute.
The visitors huffed and puffed but were unable to fashion any openings and it was Owls striker Marcus Tudgay who came closest to snatching the game's third goal when he flashed a 30-yard volley just wide in the closing stages.