Wednesday bounced back from a 5-0 drubbing at Reading last week to halt Leicester's impressive run of eight games unbeaten.
Clarke, recalled to the starting team for the first time in five games, struck in each half but his goals weren't enough to lift the Owls out of the drop zone.
Wednesday started in dramatic fashion as Clarke's shot from 20-yards was pushed round the post by goalkeeper Chris Weale.
The big striker wasn't to be denied and he broke the deadlock in the sixth minute.
Tommy Miller picked out the front man and he lashed the ball into the net from just inside the penalty area for his fourth goal of the season.
Leicester, chasing a third win on the trot, hit back as Lee Grant thwarted Martyn Waghorn as he smothered his downward header on the line after the Owls' rearguard failed to cut out a Lloyd Dyer cross.
The Wednesday keeper foiled the diminutive striker minutes later diving to his right to palm the ball away after Waghorn had conjured up a left-foot volley.
The Midlands side suffered a set back in the 31st minute as Weale suffered a suspected broken nose after colliding into Marcus Tudgay and he was substituted by Conrad Logan.
Jermaine Johnson, returning from injury, almost added a second for the Hillsborough side, twisting past his marker to fire in a low right-foot strike from just inside the box only to be denied by the diving Logan.
Clarke grabbed his second in the 61st minute after Tudgay picked out Johnson and it was his low cross from the right that found Clarke and he made no mistake.
Grant pulled off a vital save minutes later keeping out Dyer's spectacular strike before centre back Wayne Brown headed over a Waghorn corner as Leicester looked for a way back but it wasn't to be.