Jose Mourinho's side got off to a flying start thanks to John Terry's header and were already home and hosed by half-time following Willian's strike and a Jan Kirchhoff own goal.
Despite easing off after the break, substitute Didier Drogba was gifted a fourth by Willian and he then turned provider to set up fellow replacement Ramires to complete the rout.
The German outfit showed plenty of spirit when coming from behind to claim a point in a 1-1 draw at Stamford Bridge back on matchday one.
With Champions League-winning former Chelsea manager Roberto Di Matteo now in charge, Schalke also went into the game unbeaten at home this season.
But on this occasion they were simply outclassed and outplayed by the visitors' sharp passing and slick movement up front.
Schalke were still missing playmaker Julian Draxler due to a thigh injury, but Dennis Aogo returned to replace Christian Fuchs after sitting out Saturday's 3-2 Bundesliga win over Wolfsburg as Di Matteo reverted to a back four.
Mourinho signalled his intent by sticking with the same team which beat West Brom over the weekend, meaning Thibaut Courtois returned to Champions League action after being rested for both games against Maribor.
Diego Costa had an early chance on the break which Ralf Fahrmann was forced to turn away for a corner, from which Terry rose highest to head home Cesc Fabregas' set-piece with only two minutes gone.
The visitors were fortunate to stay in front when an Eric-Maxim Choupo-Moting shot deflected off Gary Cahill and over Courtois, but bounced back off the crossbar.
Chelsea continued to look dangerous with some slick passing moves on the counter-attack and they doubled their lead just before the half-hour mark when Willian fired past Fahrmann with a low shot after a neat one-two with Eden Hazard.
Costa could have made it three when intercepting a poor back-pass but the striker slipped when rounding the goalkeeper and Fahrmann did well to save an Oscar volley after a sublime chip from Fabregas.
However, Jan Kirchhoff capped off a woeful first half for Schalke by heading into his own net from another Fabregas corner to put Chelsea in total control.
The hapless Kirchhoff was hauled off at the interval and Terry did well to block an effort from substitute Christian Clemens.
At the other end, Branislav Ivanovic blasted a volley inches over the bar after a lovely cross from Willian on the break.
Just as the match appeared to be petering out, Chelsea broke away from deep and Willian unselfishly passed to Drogba to tap into an open net and the Ivory Coast forward then crossed for Ramires to head in at the far post.
Hazard was denied a sixth in stoppage time by a superb Fahrmann save but it was still a great night for Chelsea.
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