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Liverpool took the lead through Hungarian Dominik Szoboszlai (74), but City responded with goals from Portuguese Bernardo Silva (84) and Norwegian Erling Haaland (90+3, penalty).
Liverpool finished the match with 10 men after Szoboszlai was sent off (90+10).
City moved up to second place with 50 points, behind leaders Arsenal with 56 points, while Liverpool remained in sixth place with 39 points, dealing a blow to their Champions League hopes as they now trail fourth-placed Manchester United by five points.