Glen Hoddle's side arguably mustered their best performance of his short reign to rekindle their slim play-off hopes, while casting Crewe closer to the relegation zone.
Although the visitors dominated from the kick off at the Alexandra Stadium, it was the hosts who took a shock lead from the penalty spot in the 10th minute.
After David Vaughan had won a corner on the left with some dogged determination up against right-back Keith Andrews, Cort was left flapping when the flag kick was not properly cleared and his trailing arm caught the ball.
Kenny Lunt sent Michael Oakes the wrong way with the spot kick, but the home advantage lasted barely three minutes.
South Korean international Ki-Hyeon Seol had already looked dangerous roaming down the left and he breezed easily past Steve Jones' despairing challenge and aimed for the near post with a low cross, which Cort made immediate amends with by stabbing the ball home into the bottom corner.
Miller was a handful for the Crewe defence and he connected with Lee Naylor's left-wing cross with a superb diving header on 23 minutes but was a yard off from hitting the top corner of Ben Williams' net.
Joleon Lescott should have given his side the lead on the half hour when Paul Ince's corner found him completely unmarked on the edge of the six-yard box but his timid side-footer was parried away by Williams.
Yet the goal Wolves were threatening wasn't long in coming and Ince was involved again. After Miller tried to break free of Chris McCready's challenge on the right of the box, Ince went down somewhat theatrically as the Crewe defender tried in vain to block his run on goal.
Like Lunt before him, Miller had no trouble with the 34th minute spot kick as he put the ball to the other side of Williams' dive.
When debutant Darren Moss failed to clear decisively from Miller, Wolves went further ahead in first-half stoppage time. Naylor seized the ball and arced a cross to the far post where Cort ran in to thrash home his second.
Crewe came close to reducing the arrears when Jones got space on the right of the box early in the second half and when Oakes failed to hold on to the Northern Ireland international's stinging low shot, first Mark Rivers and then substitute Mike Higdon almost buried the ball home from close range.
But Williams needed to make a good stop to keep out Cort's far post volley shortly after and soon Wolves had added a fourth.
Seol twisted and turned on the left of the box and laid the ball off to Miller, who thrashed a low shot from 15 yards which went through Williams' clutches at his near post.