Championship leading scorer Cort opened the scoring when he headed in unmarked Lee Naylor's inswinging corner after 13 minutes.
It was the start of the avalanche and Glen Hoddle's side had this game killed off with still ten minutes left of the first half.
They were too powerful and disciplined for struggling Crewe although the hosts didn't help themselves with poor defending.
Miller fired in the second, an unstoppable shot, past Ben Williams from 15 yards after Naylor's driven cross deflected off a home defender. Cort was retreating suspiciously from an offside position but the goal stood.
And it got worse for Crewe when they failed to deal with Rob Edwards' right-wing cross which flew past a couple of defenders to Miller who had the simple task of tucking it home at the far post for the third.
Two minutes later tricky Korean Seol got the better of Crewe's stand-in left-back teenager Paul Bignot and Cort picked up the winger's cross before delivering a low right-footed shot past Williams.
The fourth Wolves goal prompted an exodus of home fans towards the turnstiles.
But their side had started brightly and might have suffered a different fate if they had taken a couple of early chances.
Both of them fell to Steve Jones, the first he shot agianst visiting keeper Michael Oakes' legs after being released on the right by an Eddie Johnson pass.
Then a mistake by Mark Kennedy allowed David Vaughan to break free and he set up Jones, but again the finish was poor and he dragged the ball wide of the far post.
Crewe could easily have buckled further but they showed some resistance after the break and continued to try and take the game to the visitors.
Substitute Luke Rodgers had a 78th minute goal chalked off for offside, but Leon Clarke, on for Cort, could have made it 5-0 with ten minutes left when he dragged a shot wide.