The tricky looking tie became a rather straightforward one for the Parisians, with the hosts being reduced to 10 men in the first half.
Gregory van der Wiel, Mamadou Sakho, Ezequiel Lavezzi and of course Zlatan Ibrahimovic were on target for the visitors.
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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.