The home aside took the lead on 55 minutes when Russell pounced on Ade Akinbiyi's knockdown and drilled a sweet strike into the bottom corner.
Stoke made it two when Mark Clyde was penalised for tugging Akinbiyi's shirt and Clarke converted the penalty.
Wolves grabbed a late consolation through Kenny Miller's penalty after Gifton Noel-Williams' handball.
Wolves manager Dave Jones:
"No doubt all the gloom merchants will now have a go, but the thing was we didn't do enough to win a game of football.
"Too many players on the day didn't do enough which is very unusual for us. We looked very toothless and didn't show commitment or desire to win the game.
"It was a shock to the system because it's not going to be easy and maybe one or two thought it might be.
"Maybe it's a kick up the backside that they needed. We're not in the Premiership and it's a hard division to get out of."
Stoke: de Goey, Halls, Clarke, Thomas, Taggart, Neal (Henry 79), Hall, Brammer, Russell, Akinbiyi (Greenacre 90), Noel-Williams (Asaba 90). Subs Not Used: Simonsen, Hill.
Goals: Russell 55, Clarke 70 pen.
Booked: Taggart, Noel-Williams.
Wolverhampton: Jones, Clyde, Naylor (Cooper 75), Craddock, Bjorklund (Edwards 63), Newton, Kennedy, Olofinjana, Cameron, Miller, Sturridge (Clarke 45).
Subs Not Used: Oakes, Andrews.
Goals: Miller 88 pen.
Ref: A Kaye (W Yorkshire).