Goals from Kevin Prince Boateng and Sulley Muntari give the Italian side a commanding first leg lead.
Barcelona must now find a way to win by at least two clear goals without conceding to progress.
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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.