
The result left the 13-times winners with one point after two games in Group A.
Nigerian forward Emmanuel Bonaventure stunned the Santiago Bernabeu by giving the Belgians the lead in the ninth minute, mis-controlling the ball and nudging it towards goal but somehow still beating Real keeper Thibaut Courtois to score.
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Bonaventure struck again with another scrappy goal in the 39th minute, losing his footing as he bore down on Courtois but still producing a stunning finish to lift the ball high into the net.
Real captain Sergio Ramos headed his side back into contention with a goal in the 54th minute.
While midfielder Casemiro equalised with a header in the 85th, moments after Bruges captain Ruud Vormer had been sent off.
Zinedine Zidane’s side is joint-bottom of Group A with one point, having lost 3-0 at Paris St Germain two weeks ago.
PSG won 1-0 away to Galatasaray to top the group with six points.
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