Young Nigerian forward Emmanuel Bonaventure scored two first-half goals for the Belgian club but Madrid recovered with headers by Sergio Ramos in the 55th and Casemiro in the 85th.
Casemiro’s header came from a free kick straight after Brugge went down to 10 men as captain Ruud Vormer was sent off for a second yellow card.
Madrid stayed last in Group A, two points behind leader Paris Saint-Germain, which visits Galatasaray later Tuesday. Brugge, which has never advanced to the knockout round, has two points, one more than Galatasaray.
PSG defeated Real Madrid 3-0 in the first round.
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Source: Fox Sports