Clarke, making only his fourth league start of the season, fired Wolves ahead before salvaging a point with a 73rd minute equaliser.
Wolves had won their previous three games at home but struggled to hit those heights against a Wednesday side who have been revived since the departure of manager Paul Sturrock.
Before Clarke's equaliser, they had looked set to make it two wins out of two under caretaker boss Sean McAuley after goals from the impressive Wade Small and Chris Brunt.
Wednesday arrived at Molineux without an away goal for 266 minutes and could easily have wilted after Clarke's first strike.
But their battling qualities shone through and a point was the least they deserved from an impressive display.
The Owls were unfortunate to fall behind, as they would have taken the lead themselves in the 23rd minute but for Matt Murray pulling off a stunning one-handed save to deny Marcus Tudgay.
It was a vital intervention as Wolves moved ahead seven minutes later when Jamie Clapham's pin-point cross was headed home at the near post by Clarke, who had replaced the rested Jemal Johnson.
The disappointment of falling behind only served to spark Wednesday into their best spell of the half and it was a surprise that it took them until the 36th minute to equalise.
Small was denied by Murray and then the former England Under-21 goalkeeper produced another great save to turn away Madjid Bougherra's stooping header.
But Murray was powerless to stop Small for a second time when he picked up a loose ball from Clapham and held off three challenges before lifting home his shot - the first goal Wolves had conceded at Molineux in five hours and 25 minutes.
That was a setback Wolves struggled to overcome and Brunt stunned Molineux eight minutes into the second half when he stabbed home a loose ball at the far post after Murray pushed out a drive by Small.
Wolves looked short of ideas and confidence, but the introduction of Lewis Gobern in place of the off-key Darren Potter gave them more urgency.
Clarke rescued them 17 minutes from time, but his face-saving strike was a disaster for Wednesday full-back John Hills.
He deflected a flick-on from Carl Cort into the path of Clarke who gave goalkeeper Brad Jones no chance with a swerving volley.