The Portuguese outfit won 1-0 in the Estadio do Dragao, thanks to a goal from Joao Moutinho.
Malaga must now score twice and keep a clean sheet or better to progress to the last eight on their Champions League debut.
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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.