One victory from their opening four league games left Atletico seven points adrift of Barcelona a fortnight ago but three on the spin have now steered Diego Simeone's side back on track.
From his personality to his difference of opinion in transfers, here we look at three reasons the Italian only lasted two seasons with the Blues.
FIFA World Cup 2018: Spain striker Diego Costa denies 'provocation' but admits to 'lucky' goal against Iran
Diego Costa now has three goals from two games, only one less than Portugal star Cristiano Ronaldo's tally of four.
Costa, who scored twice in a 3-3 opening draw with Portugal in Sochi, courted controversy early in the Group B encounter when he stepped on the toes of Iran 'keeper Ali Beiranvand.
Diego Costa looked like a misfit at the World Cup in Brazil in 2014, where Spain's inability to accommodate the burly centre-forward contributed to their disastrous campaign.
Cristiano Ronaldo scored a stunning hat-trick as Portugal snatched a 3-3 draw with Spain in a World Cup classic here Friday.
The home side salvaged a degree of pride when Pablo Sarabia and Nolito tucked away goals in the last five minutes.
Costa was left out of Chelsea's pre-season tour of Asia and has been training away from the rest of the first-team squad.
Costa's Instagram account was inundated with requests from Palmeiras fans to sign with the club on Monday.
Costa also said he might consider a loan move to Spain or Brazil and affirmed on ruling out China for a move.
Costa scored 22 goals this season in firing Chelsea to the Premier League title for the second time in three seasons at the club.
Diego Costa made an immediate impression in English football after arriving from Atletico Madrid in 2014.
Tianjin issued a statement saying they have had no communications or negotiations in any form with Diego Costa.
Antonio Conte has warned Diego Costa to ignore speculation about a potential move to the lucrative CSL.
Diego Costa ended a seven-game goal drought in style to help Chelsea open up a seven-point lead in the Premier League with a 4-2 victory over Southampton.