A misjudgement by David Luiz with 10 minutes on the clock allowed Jordon Mutch to steal in and edge the visitors into a surprise lead, as he raced through to collect a Ramires back-pass and dink over the onrushing Petr Cech.
Chelsea levelled in bizarre circumstances on 33 minutes, with Eto'o nicking the ball off Cardiff goalkeeper David Marshall as he bounced it inside his penalty area - in what appeared to be a clear breach of FIFA rules.
The Cameroonian striker was unable to convert himself, but Eden Hazard was on hand to crash home from close range and restore parity.
Eto'o was to get his goal, though, on 66 minutes, as he drilled low into the bottom corner, and Oscar stepped off the bench to rifle in a spectacular effort from 25 yards out on 78 minutes.
With Cardiff chasing the game, they left themselves hopelessly exposed at the back and Hazard grabbed his second of the afternoon eight minutes from time as he drifted inside off the left flank and drilled under the body of Marshall.
Jose Mourinho is now unbeaten in 64 Premier League matches at Stamford Bridge, but few can have been as incident packed as Chelsea claimed a fourth home win from four this season to extend their unbeaten run in front of their own supporters to 12 matches.
Chelsea's Portuguese tactician - who ended the game in the stands after launching a touchline blast at referee Anthony Taylor - had heaped praise on his central defenders John Terry and Luiz in the build-up, with the pair keeping England man Gary Cahill out of the side.
But the Brazil international's error let Mutch in. A Marshall goal-kick was pulled down and Ramires played the ball backwards towards Luiz, who left it and Mutch stole in to loft the ball over Cech.
Chelsea's equaliser was to prove controversial.
Marshall chose to bounce the ball with Eto'o lurking and had the ball stolen in a manner reminiscent of Gary Crosby taking the ball from Andy Dibble 23 years ago and Dion Dublin dispossessing Shay Given in November 1997.
Hazard picked the ball up and centred for Eto'o, who clumsily failed to get a shot away. The ball broke for Hazard whose shot went in with a slight deflection as Eto'o, who had just spurned a glorious opportunity for his first Blues goal, lay prone inside the six-yard box.
A look at the FIFA rules showed the officials should have disallowed the strike.
The visitors suddenly found themselves under siege, but the ball would not fall for Chelsea, who introduced Fernando Torres for left-back Ryan Bertrand.
When it did, Oscar, Hazard and Eto'o combined to devastating effect, with the latter firing in low beyond Marshall.
Cech showed why he was hailed as the world's number one goalkeeper in the build-up by Mourinho by saving spectacularly from Kim Bo-kyung as Cardiff came close to a leveller.
Then Chelsea stepped up a gear, as if to make amends for their manager's absence from the technical area, where he had spent much of the game in conversation with fourth official Trevor Kettle.
Oscar thrashed the ball high into the net from the edge of the area and, after Willian fired straight at Marshall on the counter attack, Hazard shot through the Scotland goalkeeper after cutting in from the left on to his right foot.