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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Since Guus Hiddink arrived at the helm, Chelsea have improved considerably after a tricky start to the campaign.
Newcastle United are staring down the barrel of relegation to the Championship for the second time in the past eight years.