The clash signalled a new era for Real Madrid as new boss Julen Lopetegui faced his first proper outing without the departed Cristiano Ronaldo, who left the Spanish capital for Juventus in July.
And the European champions made the worst possible start when Diego Costa out-muscled both Raphael Varane and Sergio Ramos to open the scoring with just 49 seconds gone.
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However, Madrid re-grouped and went into the interval at parity after Karim Benzema headed home from close range after fine work from Gareth Bale.
Lopetegui looked set to collect his first trophy as Madrid manager when Sergio Ramos converted a 63rd-minute penalty but Costa once again pounced, this time from close range and with a little over 10 minutes remaining, to level the tie once more.
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