Cort put the visitors ahead on 13 minutes as he headed home Lee Naylor's corner to the back post.
Scotland international Miller fired home with his left foot on 27 minutes, and made it 3-0 seven minutes later as he headed home Rob Edwards' cross.
The home side were still reeling just two minutes later as Cort converted Mark Kennedy's clever delivery.
Wolves boss Glenn Hoddle:
"It was a magnificent performance. In the first half Crewe didn't know what hit them. We came out like an express train and went 4-0 up.
"The way the team are playing at the moment it's a pleasure to watch them. We have been clinical recently.
"Other than the goals we scored we only had two real chances."
Crewe: Williams, Moss, Foster, McCready, Bignot, Lunt, Billy Jones, Gary Roberts, Vaughan, Johnson (Suhaj 70), Steve Jones (Rodgers 70).
Subs Not Used: Tomlinson, Cochrane, Rivers.
Wolverhampton: Oakes, Edwards, Lescott, Gyepes, Naylor, Cameron (Davies 72), Kennedy, Ricketts, Miller, Seol, Cort (Clarke 77).
Subs Not Used: Postma, Olofinjana, Craddock.
Goals: Cort 13, Miller 27, 34, Cort 36.
Ref: R Oliver (W Midlands).