Mackay has insisted he has no intention to quit, despite reports that Bluebirds owner Vincent Tan is also suggesting substitutions and tactics during games.
No clean sheet on Cech landmark
Petr Cech was making his 300th Premier League appearance for Chelsea but could not keep what would have been his 146th clean sheet. Jordon Mutch's goal for Cardiff was the 220th to have been scored past Cech in the league since he moved to Stamford Bridge in 2004.
Tan was not at Stamford Bridge and Mackay's tactics proved effective as his side soaked up Chelsea's attacks despite conceding the majority of possession, and frequently threatened on the break.
John Terry twice went close to levelling with headers but it took a superb save from Petr Cech to stop Peter Odemwingie extending Cardiff's lead with a header from Peter Whittingham's free-kick.
Chelsea's frustrations continued after their controversial equaliser, at least until Eto'o scored his first Premier League goal after 66 minutes by latching on to a Hazard pass and burying the ball past Marshall.
The Bluebirds responded well and almost hit back when Kim Bo-Kyung stung Cech's palms.
Cardiff 'time-wasting' angers Chelsea
Mourinho had to watch what looked like being an anxious final 20 minutes from the stands, with Taylor ordering him from his technical area after he persistently complained to fourth official Trevor Kettle about the referee's decisions.
But Oscar's fine strike from the edge of the box gave his side breathing space in the 78th minute and Hazard made it four soon after, dancing into the box before beating Marshall at his near post.
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