Carlos Vela had put Sociedad in front before Javier Saviola levelled for the Andalucians.
But a strike from Xabi Prieto won the game for the visitors, leaving Malaga in fourth.
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The reputation of the Premier League means it is the most popular and one of the most watched leagues in the world.
Five English clubs will compete in the last sixteen of the Champions League for the first time ever as Liverpool, Manchester United, Manchester City, Chelsea and Tottenham face some difficult away matches.