Czech side Plzen broke the deadlock against the run of play in just the fourth minute when Frantisek Rajtoral stroked home a loose ball.
Ten minutes later it was almost two when Daniel Kolar headed just wide after Igor Akinfeev had misjudged a cross. Moments after, Kolar played in strike partner Marek Bakos but he couldn't find the target with just Akinfeev to beat.
Plzen were made to pay for their missed chances when Zoran Tosic's deflected shot found the net in the 19th minute.
CSKA completed the first-half turnaround just before the half-hour mark when Tosic slipped in Keisuke Honda, who flicked the ball home with the outside of his boot.
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Four minutes into the second half CSKA almost made it three when Ahmed Musa hit the post from six yards out.
Plzen then could have equalised but Kolar's goalbound shot was cleared off the line by Honda.
Plzen pulled a goal back in the 91st minute when Bakos headed home after Akinfeev had punched the ball straight at him but it was too little too late as Moscow triumphed.
Plzen stay bottom of the group while CSKA draw level with Manchester City and Bayern Munich, who face off at 7.45pm, on three points.