The Portuguese league leaders put themselves in a strong position when Nicolas Gaitan struck early.
Dirk Kuyt equalised for the visitors, to give them a priceless away goal, but Oscar Cardozo struck twice to give Benfica their final place.
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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.