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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The reputation of the Premier League means it is the most popular and one of the most watched leagues in the world.
Five English clubs will compete in the last sixteen of the Champions League for the first time ever as Liverpool, Manchester United, Manchester City, Chelsea and Tottenham face some difficult away matches.