Mourinho’s side were forced to come from behind after Jordan Mutch gave the visitors a 10th minute lead in west London.
But Chelsea equalised through Eden Hazard’s 33rd minute effort and went on to win thanks to second-half goals from Eto’o, Oscar and another from Hazard.
Victory maintained Chelsea’s 100 percent home league record this season although the win was tarnished when manager Mourinho was forced to watch the final 20 minutes seated among Chelsea supporters, having been sent off by referee Anthony Taylor after reacting angrily to a series of decisions.
While Mourinho’s frustration was at least tempered by victory, Cardiff manager Malky Mackay found little relief after a difficult two weeks.
Cardiff’s preparations had been overshadowed by upheaval behind the scenes at the Welsh club amid reports of growing friction between manager Mackay and Vincent Tan, the club owner.
Tan’s decision to dismiss Iain Moody, the head of recruitment and a close ally of Mackay, and replaced him with Alisher Apsalyamov, a 23-year-old Kazakh who went to school with Tan’s son and had no prior experience in the role, angered the manager.
But Mackay insisted before this match he’d not been encouraged to resign and the manager’s popularity among Cardiff supporters was confirmed by the reaction he received when he took his seat in the dug-out.
The Scot responded with a clenched fist salute, and the bond between manager and supporters was strengthened even further when Cardiff took the lead after just 10 minutes.
Cardiff goalkeeper David Marshall launched a goal-kick downfield and the ball broke loose to Blues midfielder Ramires, who directed an underhit back-pass towards Chelsea keeper Petr Cech.
David Luiz failed to react and Mutch nipped in to stroke the ball home.
Chelsea pressed for an equaliser, with John Terry twice heading narrowly wide although they were forced to call on Cech to keep out Peter Odemwingie’s header.
But Cardiff may well have reached the interval with a confidence boosting lead had Marshall not been caught out by Eto’o who nipped in to poke the ball away as the keeper bounced the ball.
That freed Hazard inside the visitors’ area but Chelsea still came close to spurning the chance when the Belgian attempted to tee up Eto’o who was caught in possession and relieved to see the ball break again for Hazard who finished from close range in the 33rd minute.
Back on level terms, the home side moved through the gears and always looked the likelier winners.
Cardiff were forced onto the back foot from the start of the second half with Marshall quickly called into action to repel an Eto’o drive.
Then Juan Mata should have done better with an acrobatic volley from Ryan Bertrand’s cross.
The next Chelsea goal was clearly on the way and it arrived when Hazard, allowed too much time on the edge of Cardiff’s area, found Eto’o with a clever reverse pass.
And the striker finally broke his Chelsea duck after drifting past one defender and beating Marshall with a powerful drive.
Eto’o’s celebration spoke volumes about the player’s relief after struggling to adapt to life in the Premier League following his arrival from Russian side Anzhi Makhachkala.
From that moment on, Chelsea were in cruise control and Mourinho’s dismissal did nothing to halt their flow.
Oscar added a third in the 78th minute with an excellent dipping drive from 25 yards and Marshall’s misery was complete when he allowed Hazard’s 82nd minute shot to squirm under his body.