Derek Riordan had fired Hibs in front with a typically clinical finish but missed a great chance to seal the points before Clarkson struck.
Visitors Motherwell kicked off on a blustery Edinburgh afternoon where the sides also had to contend with an appalling playing surface that was bare in areas and patchy in others.
But Hibs made light of the conditions with a fabulous goal after eight minutes. Home debutant Denes Rosa sent John Rankin to the byline and his cut-back was inch perfect for Derek Riordan to side-foot into the top corner from 12 yards.
Motherwell battled back and Rob Jones did well to block from Stephen Hughes before heading a dangerous cross from Alan O'Brien clear.
And Hibs almost profited from indecision by Graeme Smith as he stayed on his line while Riordan chased a long high ball from Jones. But the striker couldn't gather the ball and Well survived.
Grzegorz Szamotulski showed good positioning to hold Steven Hammell's free-kick from 25 yards that moved in the wind and the Polish keeper was in action again to pluck a dangerous cross from Jim O'Brien out of the air.
A quick throw-in by Rosa gave Riordan a yard of space and, although he found a good cross, there were no takers in the six-yard box.
And Riordan threatened again with a free-kick seconds before the interval. He got the ball over the Motherwell wall only for it to sail over the bar.
Motherwell enjoyed a spell of possession at the start of the second half and O'Brien forced a fine save from Szamotulski low to his left with a close-range volley.
But a break out of defence with Rosa and Riordan linking almost earned Hibs a goal as the latter fed the Hungarian and he dragged his finish narrowly wide.
And only a fine block by Mark Reynolds prevented Riordan' volley from 15 yards flying past Smith as Hibs created the clearer chances.
Indeed a neat move between Joe Keenan and Riordan resulted in the striker firing just over the bar again.
But Well should have levelled when Clarkson's excellent cut-back found Jamie Murphy 12 yards out but the youngster fired wide with the goal at his mercy.
The equaliser came in the 77th minute minutes when Steven Thicot pulled over Murphy needlessly in the box and Clarkson fired the penalty powerfully past Szamotulski.
And despite a frantic finish neither side could clinch the win.