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Former Chelsea player Andre Schurrle was the man to give Wolfsburg all three points as the German side now reside two points above Manchester United, who play PSV Eindhoven this evening.
The game in Russia was rather uneventful in the early stages as both defences were able to frustrate their opponents.
Bas Dost had two early chances to get on the scoresheet - a header that ended up drifting wide of the post and a shot that flew into the stands.
After the break, CSKA came out fighting as they earned a quick corner and free kick, but neither play was able to get past visiting keeper Diego Bengalio.
Maximilian Arnold tried his hand at breaking the deadlock with a 25-yard half-volley, but Akinfeev managed to drop down to stop the strike.
At the other end, the home side came inches away from taking the lead when Zoran Tosic's effort from the edge of the box clattered off the post.
That particular effort was rued by the CSKA players as minutes later substitute Schurrle, who collected the ball off Dost after it was hoofed over the top, knocked the ball from a tight angle at Akinfeev.
The goalkeeper, who has not kept a clean sheet in his last 31 Champions League matches, failed to get the ball as it slipped under his arm and into the back of the net.
Immediately after going a goal down, CSKA tried to respond as Ahmed Musa found plenty of space on the left before sending a thumping cross into the box, but the Wolfsburg defence eventually cleared.
Schurrle ended any hope of CSKA getting back into the game as he sent the ball into the bottom corner of the net on the half-volley.
The visitors controlled the middle of the park and their Russian opponents failed to make the most of any chances that fell their way.