Wolverhampton Wanderers 1 Plymouth Argyle 0
Clarke had last scored way back in August in the 2-2 draw at Cardiff City.
He finally returned to the goal standard in the 26th minute of an encounter that Wolves really should have won by a far more convincing margin.
They dictated the game against a Plymouth side who were forced to play with Micky Evans as a lone striker due to their injury problems
Plymouth, who had ground out an impressive draw at Molineux last weekend, spent almost the entire 90 minutes on the defensive.
Goalkeeper Romain Larrieu produced another fine display for Plymouth but it was not enough to prevent their elimination from the cup.
It was a major surprise that Wolves needed 26 minutes to break the deadlock as they dominated the game from the kick-off.
Mark Davies and Colin Cameron both went close while it needed a goalline clearance from Akos Buzsaky in the 24th minute to keep out a powerful header from his fellow Hungarian Gabor Gyepes.
Plymouth's resistance was finally broken in the 26th minute when Cameron swung in a cross from the right wing.
The centre caught the Plymouth defence flat-footed and Clarke coolly slotted the ball home from eight yards.
Wolves would have added to their advantage before half-time if it had not been for the impressive Larrieu.
He pulled off a smart 28th minute save from Kenny Miller and then tipped a long-range drive from Cameron over the bar on the stroke of half-time.
Such was Wolves' domination that it was first-half stoppage time before Plymouth tested goalkeeper Stefan Postma who easily dealt with a shot from Buzsaky.
Buzsaky really carried Plymouth's only threat and he was inches away from grabbing a shock equaliser in the 55th minute when another long-range drive dropped on to the roof of the net.
But that signaled the end of Plymouth's challenge as Wolves comfortably held on to the advantage to book their place in the fourth round.