Captain John Terry headed in a corner after 78 seconds and Brazil midfielder Willian doubled the lead with a fierce low shot on the half hour.
A Jan Kirchhoff own goal in the 44th minute made it 3-0 and second-half goals from substitutes Didier Drogba and Ramires allowed Chelsea to extend their unbeaten start to the season to 19 games in all competitions.
“It was a fantastic performance from the first to the last minute…5-0 in Germany is not normal,” coach Jose Mourinho told reporters.
“Any team would have struggled against us tonight with the quality we showed.”
Schalke, who hit the woodwork in the first half, had little to offer against a rampant Chelsea as coach Di Matteo lost his first meeting against the team he led to Champions League glory in 2012.
Chelsea clinched top spot in Group G with 11 points from five games, four ahead of Sporting who beat Maribor (three) 3-1 on Tuesday.
Schalke, who lost for the first time at home under Di Matteo, are in third position on five points with one match remaining.
“I’m at a loss for words,” said Schalke captain Benedikt Hoewedes. “I can only apologise to everyone. We gave Chelsea too much space to play.”
Diego Costa, who has scored 11 goals in 10 games in this season’s Premier League but none in Europe, raced clear in the first minute but had his shot blocked.
The resulting corner, however, saw Terry beat Hoewedes in the air to give his side a dream start.
Mourinho, bidding to become the first coach to win the Champions League with three different teams, wanted a trouble-free victory to ease the pressure going into a busy period of fixtures and that is precisely what his side gave him.
Chelsea were lucky when Eric Maxim Choupo-Moting’s deflected shot bounced off the crossbar but Willian put the hosts firmly in their place with a second goal.
The unfortunate Kirchhoff then headed a left-wing corner, from the outstanding Cesc Fabregas, into his own net on the stroke of halftime.
Drogba tapped the ball into an empty net after being set up by Willian before the Ivorian lofted the ball to the far post for Ramires to nod the fifth goal for the runaway Premier League leaders.
Chelsea’s victory equalled their best Champions League away result, 5-0 at Galatasaray in 1999. (Reuters)