Clarkson converted a penalty with 15 minutes remaining following substitute Steven Thicot's foul on Jamie Murphy.
Hibs had taken the lead in the eighth minute when Derek Riordan found the net with a composed finish from 10 yards from Ross Chisholm's cut back.
Despite making a solid start to the game, Motherwell fell behind inside 10 minutes.
After making ground down the left flank, Chisholm picked out the unmarked Riordan with a cut back from the byline and the Scotland international made no mistake with a well-placed left-footed shot from 10 yards.
Motherwell then laid siege to Hibs' goal in the hope of making a quick response. After Clarkson forced his way into the box and had a shot blocked, Stephen Hughes saw an effort from the edge of the box cannon off Rob Jones.
A further attack came to nothing as Hibs lived dangerously.
There were fears over captain Jones' continued involvement in the match after he appeared to pick up a hip injury but the Englishman returned to the action after receiving treatment.
Motherwell were given the chance to test Hibs goalkeeper Grzegorz Szamotulski after Chris Hogg gave away a free-kick 30 yards from goal.
Left-back Stevie Hammell curled an effort over the wall but Szamotulski positioned himself well and easily collected the shot.
A blustery wind coupled with a threadbare pitch ensured the conditions for both sets of players were far from ideal.
On a rare foray into the Motherwell box, Riordan brilliantly flummoxed Mark Reynolds with his close control but his shot was deflected clear.
With four minutes of the half remaining, Hibs were awarded a free-kick in a central position 35 yards from goal following a foul on Colin Nish but Riordan fired the ball well over the bar.
Hibs manager Mixu Paatelainen made a minor alteration at the break with Steven Thicot replacing Chisholm.
Frenchman Thicot was immediately involved in the thick of the action, making a timely challenge on Marc Fitzpatrick as the midfielder stormed into the box.
Another free-kick at a favourable angle for Hammell to have a shot was awarded 25 yards out but again the left-back struck straight at Szamotulski.
Motherwell began the second half with a purpose about their play and were enjoying the lion's share of possession.
It was no surprise that the next chance fell to Motherwell in the 58th minute. Clarkson played a one-two with Jim O'Brien before drilling a left-footed shot at the near post from close range but Szamotulski palmed the ball wide.
From the resulting set-piece, Denes Rosa's punt from the edge of the box set Riordan clear on the counter-attack, Rosa received a return pass from the striker after sprinting up the park but his deft chip over Graeme Smith just missed the target.
Riordan was involved again minutes later when substitute Joe Keenan's cross fell to him but his volley was well saved by Smith.
Following patient build-up play, Riordan then hit a shot over the bar from 15 yards after taking the ball off the feet of Keenan.
Motherwell wasted a superb chance to level in the 70th minute when substitute Jamie Murphy placed a shot wide from eight yards after Szamotulski had been tempted out of position from Clarkson's pass across the box.
Right-back Paul Quinn was denied from close range by Szamotulski moments later, driving into the box between Jones and Paul Hanlon after taking Stephen Craigan's throw-in first time.
The visitors finally made their pressure count in the 75th minute when Clarkson equalised from the penalty spot.
Thicot was guilty of giving away the spot kick after pulling on Murphy's jersey and Clarkson converted from 12 yards.