The hosts were cruising after a dominant first-half display and goals from Ahmed Musa and a double from Seydou Doumbia put them 3-0 up at halftime in the Group B encounter.
Yet Maxime Lestienne scored twice within eight minutes after the break as the visitors launched a fine comeback that almost allowed them to snatch a point, before they were halted in their tracks by an 80th-minute red card for Santiago Arias.
All four teams in the group are on three points after their opening two games after Manchester United beat VfL Wolfsburg 2-1 in the other match.
The Russian side took the lead after seven minutes when the impressive Musa was on hand to stab the ball into the net from close range after PSV failed to clear Zoran Tosic's corner.
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Leonid Slutskiy's team doubled their advantage on 21 minutes following a fine team move, involving great interplay between Mario Fernandes and Tosic, which released the Brazilian down the right flank.
His inch-perfect cross picked out Doumbia, who headed past PSV keeper Jeroen Zoet.
Doumbia made it 3-0 from the spot after Tosic was fouled, but the Ivorian wasted a chance for a hat-trick when he blasted a second penalty over the bar a minute before halftime, following a foul on Musa.
PSV were rejuvenated in the second half and took the game to CSKA.
Lestienne was instrumental as he turned in Adam Maher's cross from close range to give the visitors hope.
Lestienne, who had never previously scored in the Champions League, grabbed his second with a thunderbolt shot, which he rifled past CSKA keeper Igor Akinfeev on 68 minutes, but the visitors' comeback hopes were dampened by Arias's late dismissal.
(Reporting By Dmitriy Rogovitskiy; editing by Toby Davis)
