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 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.
With the hosts unable to find a breakthrough in the first 45, the nerves amongst the home fans were palpable after the restart, and they were not helped when Musa pulled a shot narrowly wide with Zoet beaten after being set up by Kirill Nababkin on the hour mark.
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The match finally sparked into life with a quarter of an hour remaining as CSKA put PSV on the brink of elimination when Sergei Ignashevich converted from the spot after Tosic won a penalty.
However, just 90 seconds later De Jong beat the offside trap to slot home from Jorrit Hendrix's knock-down, and the late drama was complete with five minutes to go when Davy Propper drilled home to lift the roof off the Philips Stadion and send PSV through at Manchester United's expense.