Clarke played for Pulis last season during a loan spell at Plymouth. But there is little doubt that he never produced the kind of finishing at Home Park that he came up with to end Stoke's three-game unbeaten away run with his first goal of the season.
Clarke, who was making his first Molineux start of the campaign, struck with a classy 21st minute strike as Wolves bounced back to form following successive defeats against Derby and Barnsley.
Nigerian international midfielder Seyi Olofinjana then ended Stoke's resistance with a powerful 69th minute header.
The defeat has only served to heap more pressure on Pulis who admitted before the game that he was struggling to win over certain sections of the Stoke fans following his return to the club this summer.
Stoke have won just once this season and their problems are clear. They have only scored eight goals this term and not even the debut of new striker Ricardo Fuller could boost their attacking intent.
To add to their problems central defender Clint Hill was dismissed in the 82nd minute after collecting two yellow cards in the space of three minutes.
It could have been different had Mamady Sidibe and Darel Russell taken advantage of their early chances. But Clarke put paid to all that with a sublime piece of skill.
There appeared to be little danger when he collected a pass from Olofinjana. He was surrounded by three Stoke defenders but proceeded to waltz past them as if they weren't there before firing a low right-foot drive past the outstretched hand of goalkeeper Steve Simonsen.
It sparked a purple patch for Wolves with Jemal Johnson twice forcing smart saves from Simonsen.
Wolves' failure to add to their advantage could have proved to be costly as Stoke built up a head of speed in first-half stoppage time - only to be denied by the in-form Murray.
Murray, whose form this season has attracted the attention of England scouts, palmed away a shot from Luke Chadwick and then frustrated Sidibe.
Half-time came at the wrong moment for Stoke and they never again posed the same threat in attack. Wolves should have doubled their advantage after 65 minutes when Craig Davies saw his goalbound shot blocked by Danny Higginbotham.
But they did not have to wait long to seal their success when the unmarked Olofinjana powered home a close-range header from Rohan Ricketts' inviting cross.