The Cameroon striker scored his first goal in Europe for the Blues on 31 minutes after a bad mistake from visiting goalkeeper Hildebrand, and fired in a second nine minutes after the break.
There was time for Eto'o's replacement Demba Ba to get on the scoresheet too seven minutes from time as Chelsea took control of Group E by matching their margin of victory in Gelsenkirchen on Matchday Three.
Following Saturday's 2-0 Premier League defeat at Newcastle, Blues boss Jose Mourinho made six changes to his starting line-up. Gary Cahill, Cesar Azpilicueta, Andre Schurrle, John Obi Mikel, Willian and Eto'o came in, with David Luiz, Ashley Cole, Juan Mata and Frank Lampard dropping to the bench.
Fernando Torres was missing with a leg injury, but there was some confusion over why Eden Hazard was left out of the matchday 18. Before kick-off, Mourinho said the Belgium winger had missed an important pre-match session and that "he couldn't train" but would not confirm any injury. Hazard watched the match from behind the home dugout.
He saw the visitors make an excellent start. Highly-rated young Germany midfielder Julian Draxler pulled a low shot just wide of the post and shortly afterwards, his Hungarian team-mate Adam Szalai also fired past the same upright. Christian Fuchs also powered a drive across the face of goal as Schalke set about Chelsea early on.
After Draxler was booked for fouling Azpilicueta, Chelsea found their rhythm and enjoyed some long spells of possession before opening the scoring on 31 minutes courtesy of Hildebrand's howler.
The goalkeeper pondered too long before deciding where to aim his clearance kick and was closed down on the edge of his own box by Eto'o, who got his foot in the way and sent the ball back over the Schalke goal-line. The 32-year-old celebrated enthusiastically with Mourinho.
Willian and birthday boy Schurrle almost linked up successfully before the break, but Chelsea only had to wait six minutes into the second half before doubling their lead.
The fine margins were emphasised for Schalke as Petr Cech had to make a sharp save low down to his right after Draxler cut inside Azpilicueta. Chelsea broke, and Willian burst through the midfield before passing right for Eto'o. His first touch was sublime and allowed him to quickly strike a firm shot across Hildebrand and inside the far post.
Schurrle then saw his whipped effort beaten away by Hildebrand, and Oscar had the ball in the back of the net only to be foiled by the offside flag.
Initiated by an injury to Draxler, Schalke made their three substitutions in the space of 15 minutes, and Chelsea then followed suit within four minutes - Ba, Kevin De Bruyne and Lampard replacing Eto'o, Schurrle and Oscar respectively.
Ba got an early sight of goal soon after coming on following Ramires' pass but dallied too long. However, he was then able to notch his first Champions League goal on 83 minutes.
After Ba's good chest control, Willian kept the move alive and Lampard played the ball over the top. Ba adjusted his body shape to get a shot away, and saw his effort roll over the line.
With Basel drawing 1-1 with Steaua Bucharest in the other game in Group E, Chelsea top the table on nine points, with Schalke second on six, Basel third on five and Steaua bottom on two.
Mourinho's men return to league action at home to West Brom on Saturday, with their next Champions League assignment against Basel at St Jakob Park on Tuesday, November 26.