Goals from Keisuke Honda and Ahmed Musa gave them a crucial win that means that CSKA have seven points from three games.
Leaders Spartak Moscow maintain their 100% record with a 4-1 win in another Moscow derby away to Dynamo.
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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.