Real Madrid lost ground on rivals Barcelona after they failed to beat Malaga, despite having several chances to score against Los Boquerones.
The hosts thought they had taken the lead inside the opening 10 minutes when Luka Modric's pinpoint cross was met by Cristiano Ronaldo, who turned the ball into the net. However, the Portuguese attacker had scored from an offside position.
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Ronaldo then went close again moments later as he latched onto Marcelo's menacing delivery, but his diving header flew over the bar.
Juan Carlos squandered a golden opportunity to give the visitors a shock lead at the Bernabeu on the half-hour mark when he missed the target from Nordin Amrabat's cross before Jese brought a save out of Carlos Kameni at the other end.
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Within moments of the restart, Malaga had another opportunity to edge in front as Recio's free kick forced Keylor Navas to produce a flying save.
Around the hour mark, Real went close again through Ronaldo and Jese, but neither could score as Malaga stayed on level terms.
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The away side's hopes on snatching a point suffered a setback when Amrabat was sent off for throwing an arm into the face of Marcelo.
Ronaldo then missed from close range as Madrid tried to force a late winner, but the hosts appeared to be short on luck.
Los Merengues put the ball into the net again in the dying moments via Isco's shot. However, it was also ruled out for offside as Malaga left the Bernabeu with a point.
