Clayton Donaldson had fired the hosts into an 11th-minute lead on his belated home debut, before they were stunned by three quick-fire goals in just seven minutes as Well ran riot.
David Clarkson, Keith Lasley and a brilliant 25-yard lob from Ross McCormack had McGhee's outfit 3-1 up by the 24th minute as Hibs fell apart in defence.
A late Chris Porter goal - his fourth since his move from Oldham - sealed the club's place in the quarter-finals, before Mickael Antoine-Curier netted a consolation.
McGhee, who took over at Fir Park in the summer, said: "We turned our good play into goals.
"I think we probably should have scored more, but you're only going to take a certain percentage of any chances and I think we've got to be fairly satisfied with four.
"It's the best we've played this season. In other games it's been there in spells, but we're pleased how quickly they have grasped the way we want them to play.
"In the first half, I don't know if it can get any better for us than that. I hope we're not peaking too early."
McGhee, who even joked it was "a bit like watching Brazil" in the opening 45 minutes, reserved special praise for ex-Rangers forward McCormack who tormented throughout.
Ahead of facing the Ibrox side at Fir Park this weekend, he added: "Ross looked fantastic in pre-season but he injured his arm in the last pre-season game against Nottingham Forest and missed the first three games of the season.
"We've been trying to work him hard in training to get up to speed again and he looked to benefit from it here"