Atletico Madrid took three points from Balaidos despite a strong Celta Vigo performance, moving up to third in the table.
Kevin Gameiro hit the only goal, ramming home from a corner on one of the few chances Diego Simeone's side created.
Celta impressed, even with the big River stand closed for safety reasons, and hit the bar through Iago Aspas, as well as forcing Jan Oblak into some good saves.
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They could have had a penalty when the ball struck Gabi's hand in the box, although it was from close range.