Seol Ki-Hyeon set up Cort to fire home from close range, and the Korean was the provider again just after the break for Miller to head Wolves 2-0 up.
When Gabriel Ngalula Mbuyi brought down Cort, Lee Naylor lashed in a 30-yard free-kick to wrap up the points.
Wolves boss Glenn Hoddle
"It was a magnificent performance. Stoke are a good team and this is a difficult place to come, but we've played tremendous stuff.
"It was the best display since I became manager and we will take some stopping if we continue in that vein.
"We can't afford to let Sheffield United get too far ahead, but every team has a wobble."
Stoke: Simonsen, Buxton, Hoefkens, Duberry, Broomes, Chadwick (Harper 45), Brammer (Mbuyi 66), Russell, Kolar (Dyer 71), Gallagher, Sidibe.
Subs Not Used: de Goey, Halls.
Goals: Buxton 90.
Wolverhampton: Oakes, Edwards, Lescott, Gyepes, Naylor, Seol, Cameron, Ricketts, Kennedy, Miller (Ndah 85), Cort.
Subs Not Used: Postma, Olofinjana, Craddock, Davies.
Goals: Cort 42, Miller 48, Naylor 73.
Ref: M Atkinson (W Yorkshire).