Goals from Mathias Pogba, Mark Ellis, Chuks Aneke and Luke Murphy usurped the 13th-minute lead given to the visitors by Matt Spring's rasping shot.
Despite losing skipper Gary Doherty to a ninth-minute injury, Wanderers were on top in the opening half hour and may have extended their lead had substitute Richard Logan connected with a cross right in front of goal.
But Pogba levelled matters up in the 19th minute when he pounced after goalkeeper Jordan Archer could only parry an Aneke effort. Ellis then followed up a header with a close-range finish to edge Crewe ahead five minutes before the break.
Archer kept the score down with a super performance and saved a 52nd-minute penalty from Harry Davis after Pogba had been brought down inside the box. The Tottenham loanee flung himself across to his right to keep out the centre-half's spot kick.
But the 19-year-old was given no chance with fierce drives from Aneke, after 62 minutes, and Murphy 15 minutes later which flew into the top corner to underline Crewe's superiority.