Iran Press/ Europe: Atleti got off to a perfect start when Samuel Lino's inswinging cross from the left flank was flicked home by Morata's header in the fourth minute.
The lead was then extended when Antoine Griezmann jumped backwards to steer home Saul Niguez's cross home.
Real had a lot of possession but mainly threatened through long-range shots and one of these from Toni Kroos was impossible for Jan Oblak to keep out as he dived in vain to his right side.
The visitors were the better side going into half-time but a minute after the restart Atleti were back in front when Saul's perfect cross was nodded home by Morata for their third headed goal of the day.
The closest Real came to reducing the scoreline were through Aurelien Tchouameni and Antonio Rudiger while Mario Hermoso saw a header flick off the crossbar at the other end of the pitch.
The result leaves Real Madrid third in the table, while Diego Simeone's side rise to fifth.
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