The Polish forward scored early on to put the German side ahead but Cristiano Ronaldo had levelled by half time.
But Lewandowski pounced on a loose ball in the box twice to make it 3-1 before netting a penalty to wrap up an emphatic victory.
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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.