Mourinho’s Premier League leaders brushed Di Matteo’s ineffective Royal Blues aside in Gelsenkirchen as captain John Terry put them ahead within just two minutes of the kick-off.
Further first-half scores by Willian and an own goal from defender Jan Kirchhoff was followed by second-half strikes from Didier Drogba and Brazil midfielder Ramires.
The result fell just short of Schalke’s record European home defeat when they were hammered 6-1 by Real Madrid in last season’s round of 16, first leg, in February this year.
Chelsea remain unbeaten in all 19 matches this season and are now four-points clear in the table ahead of their final match at home to second-placed Sporting Lisbon in a fortnight.
Schalke drop to third, having been leap-frogged by Sporting who won 2-1 at home to Maribor, who they now face away in Slovenia in their final game next month.
Di Matteo, who is just eight games into the Schalke job, remains the only Chelsea manager to win the Champions League title and Mourinho refused to even talk about him in the match’s build-up.
The self-styled ‘Special One’, who won the Champions League with Inter Milan in 2010 and Porto in 2004, is bidding to win the European crown at the fifth attempt with Chelsea and his side dominated their hosts in Gelsenkirchen.
Chelsea needed less than two minutes to take the lead at Schalke’s Veltins Arena.
Eden Hazard put Diego Costa away and the Spain striker tested Schalke goalkeeper Ralf Faehrmann, who palmed his shot away.
Cesc Fabregas floated in the corner from which Chelsea captain John Terry rose highest to head home barely challenged.
Cameroon striker Eric Choupo-Moting gave Schalke brief hope on 13 minutes when his shot deflected off Gary Cahill’s boot and looped over Chelsea goalkeeper Thibault Courtois, but clattered off the bar.
Chelsea were unpicking the Schalke defence with worryingly ease as they doubled their lead.
Hazard timed his pass to Willian perfectly and the Brazilian’s low drive shot under Faehrmann’s dive on 28 minutes to put the guests 2-0 up.
Booes and whistles echoed around the Veltins Arena by the time defensive midfielder Jan Kirchoff turned the ball into his own net on 44 minutes and raised to a noisy crescendo when the referee ended a miserable half moments later.
With his side facing eight games in a busy December period, Mourinho replaced Costa, who has netted 11 goals this season, with veteran forward Didier Drogba with an hour gone.
He scored their fourth when Fabregas put through a superb pass to Willian, who squared to present Drogba with a simple tap in on 76 minutes.
The guests fifth goal followed just two minutes later as Drogba crossed for Ramires, who out jumped the porous home defence.
Only good keeping by Fahrmann denied Chelsea replacement Andre Schuerrle, then Hazard, in the final five minutes as the guests hunted a sixth goal.
The home side were again booed at the final whistle.