The Parisians could have won the league with just two more victories but were made to wait for the first after Gael Danic put the visitors ahead.
Paris St Germain equalised through Alex late on but they could not force the breakthrough thereafter.
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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.