Chelsea had to come from behind after a mistake from David Luiz allowed Jordon Mutch in to clip the ball over Petr Cech, who was making his 300th Premier League appearance.
Chelsea's equaliser was a result of an error of judgement from referee Anthony Taylor.
David Marshall bounced the ball in front of Samuel Eto'o, who simply stuck out a leg to nick it, even though FIFA rules state the goalkeeper is still in possession at that point.
Eto'o then contrived to miss after receiving a pass from Eden Hazard, who netted while the Cameroon striker was on the floor.
Eto'o did claim his first Chelsea goal midway through the second half and Oscar and Hazard, with his second, wrapped up victory.
The third and fourth goals came after Mourinho was dismissed from the touchline for berating the officials to a chorus of "Jose Mourinho, he sits where he wants" as the manager took a seat behind the dugout.
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 home run to 12 matches.
It was a breathless start to the first of five Chelsea games in 15 days, with the crucial Champions League Group E clash at Schalke next on Tuesday.
Cardiff won in west London last month through Mutch's stoppage-time strike but there was no repeat of the late hurrah at Fulham as the visitors were soundly beaten.
Cardiff boss Malky Mackay made a point of applauding the visiting fans before kick-off after a fraught international break in which his head of recruitment Iain Moody was replaced by 23-year-old Kazakhstani Alisher Apsalyamov on an interim basis.
Apsalyamov, thought to be a friend of the son of Cardiff owner Vincent Tan, was in the directors' box at Stamford Bridge as the visitors took a shock early lead.
Mourinho 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 defender's error let Mutch in.
A David 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 the onrushing Cech.
Cardiff had to defend doggedly to protect their advantage and Terry twice headed wide from Mata corners.
Cardiff had opportunities, too, and Cech had to acrobatically claw away a flicked-on Peter Odemwingie header.
Worryingly for Chelsea, Cardiff then won four successive headers unchallenged in the hosts' area, the last of them seeing Aron Gunnarsson head over Cech's bar.
Chelsea's equaliser was 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.
Marshall was booked nine minutes into the second half for wasting time over a Cardiff goal-kick as he attempted to give his defence a breather.
The visitors were 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, the striker 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 an equaliser.
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.
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