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CSKA looked to get off to a quick start with a shot inside the opening minute, but Zoran Tosic's effort from the edge of the box went high of the crossbar.
Daniel Kolar had the first chance of the night for the hosts, unleashing a powerful strike from just outside the penalty area, but the tight angle was too much for the Plzen striker.
Ahmed Musa came close to breaking the deadlock early in the second half, but his low shot three minutes after the restart was saved, before a second effort was smashed high.
However, Musa was able to grab a goal in the 65th minute to put the away side in front, after Keisuke Honda picked him out with a well-weighted cross, giving him an easy header.
The home side did manage to get back on level terms though, as Kolar headed into the top corner from a Pavel Horvath delivery with 15 minutes left to play.
Both teams had chances to secure a winner in the closing stages of the game, but it was Tomas Wagner who found the deciding goal for Plzen, smashing it in from close range in stoppage time.
Pontus Wernbloom was the second player to be sent off for the visitors for kicking out while Honda was lining up a free kick.
The result ensures that Plzen finish third in their group.