Alaba registered his first goal since joining Real over the summer when he fired past Marc-Andre Ter Stegen just after the half-hour mark.
Vazquez doubled the advantage for Carlo Ancelotti’s men in the third minute of stoppage time with a close-range finish, before substitute Sergio Aguero opened his Barca account by pulling a goal back with almost the last kick of the contest.
It made it three defeats from three Clasicos as Barca boss for Koeman, whose side have a La Liga record this term showing 15 points after eight matches.
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