With the group's top two Wolfsburg and Manchester United facing each other, PSV knew that victory would see them progress to the last 16 regardless of the result in Germany, and in an edgy opening they had the first half-chance when Gaston Pereiro fired wide from distance.
CSKA showed their first real sign of attacking intent after 10 minutes when Ahmed Musa burst into the penalty area down the left, but he could not direct his effort on target from a tight angle as he tried to beat Jeroen Zoet at the goalkeeper's near post.
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The Russian side were visibly growing in confidence as the half wore on, and only a challenge from Jeffrey Bruma prevented Seydou Doumbia getting a shot off after the striker had turned away from his marker.
PSV top scorer Luuk de Jong should have added to his 18 goals in all competitions so far this season and given his side the lead after half an hour when he met Hector Moreno's fine cross from deep but could only head straight at Igor Akinfeev from 12 yards out.
Zoet's fine save prevented Zoran Tosic's free kick from giving CSKA the lead, but it was PSV who should have broken the deadlock in first-half stoppage time when Bruma could only head off target from Andres Guardado's corner under little pressure from the defence.