Memphis Depay opened the scoring for the Dutch side in the 13th minute before Florian Jozefzoon wrapped up the win with a late strike.
The result lifted PSV off the foot of the group after Dinamo Zagreb were beaten 3-0 at Ludogorets in the other match.
Ola Toivonen set PSV's stall out early when he fired a 30-yard strike at Chornomorets goalkeeper Dmitri Bezotosny in the ninth minute.
The visitors were ahead four minutes later when Depay beat Bezotosny from 25 yards and found the top right-hand corner, with Zakaria Bakkali providing the assist.
Oleksiy Antonov saw his long-range effort go wide at the other end while Ivan Bobko's strike flashed over the bar as the Russians found no luck from distance.
Antonov again saw his shot miss, this time over the bar, before Franck Djadjedje's close range effort was blocked by Jeffrey Bruma.
PSV goalkeeper Przemyslaw Tyton then denied Kirill Kovalchuk and Leo Matos before he made a brilliant save to deny Oleksiy Gai.
Despite the home side's best efforts, it was PSV who were the next to score, with Jozefzoon's 87th-minute goal enough to seal the win for the Eindhoven-based club.
Goalscorer Depay turned provider to set up the substitute striker to kill off the tie and record his side's first points of the campaign.