Jose Mourinho's men responded to their shock weekend defeat with a comfortable win over their German rivals, leaving them in a fine position to qualify from Group E.
The visitors' experienced goalkeeper, Timo Hildebrand, paid the price for dwelling on the ball in the first half when his belated attempt at a clearance hit Eto’o and went into the back of the net.
Eto’o was the scourge of the Schalke keeper once again after the break, the Cameroon striker converting only his third goal for Chelsea, and his replacement Demba Ba scored his first of the season to ensure Jose Mourinho's men moved clear atop Group E.
Chelsea has won all three Champions League games since losing its opening fixture against Basel and this was its 100th victory in UEFA competitions.
Schalke, by contrast, suffered a first defeat in eight away games, but remains second giving the club a great chance of repeating last season’s achievement of reaching the knockout stages.
Eden Hazard was not even on the bench and Eto'o replaced the injured Fernando Torres (thigh) as Chelsea boss Jose Mourinho reacted to Saturday's 2-0 defeat at Newcastle by making six changes to his starting lineup.
Schalke manager Jens Keller opted for the experience of Jermaine Jones in midfield over teenager Max Meyer and striker Adam Szalai was fit despite requiring an ear operation after Saturday's win at Hertha Berlin.
Mourinho was baffled by his side's display at Newcastle and must have been scratching his head again in the first five minutes as Schalke spurned two opportunities.
Petr Cech could only watch as Julian Draxler's right-footed strike flashed just past the far post and the Germany midfielder then set off on an incisive run before setting up Szalai, who also fired narrowly wide.
Chelsea started to get into its stride and Hildebrand gifted them the lead after 31 minutes as Eto'o charged down the 34-year-old's kick.
The lively Draxler came close once again early in the second period when he cut in from the right and lined up a measured left-footed strike, but Cech made a fine fingertip save.
Chelsea doubled its lead nine minutes into the half as Willian surged forward and played in Eto'o. The former Barcelona striker beat Hildebrand with a clinical right-footed finish across goal.
Ba then got in on the act when Frank Lampard set him up for a well taken left-footed volley seven minutes from the final whistle.