The away side started the match superbly with two strikes in the opening 10 minutes, and the Turkish hosts were unable to get back in the game
The Eindhoven giants picked up an early lead via Tim Matavz, before Ola Toivonen doubled their lead shortly after. Olcan Adin then pegged one back for the Turks, but they were unable to level the scoring in the remainder of the game.
The hosts started the match with attacking intentions, and almost got the early opener they were after. Nevertheless, Burak Yilmaz's powerful long range strike was tipped over the bar by PSV goalkeeper Andreas Isaksson.
PSV then grabbed the lead in the sixth minute after a brilliant individual move from Matavz. The Slovenia international received the ball some 25 yards away from the Trabzon goal, turned past his opponent, and found the top corner with a left-footed strike from the edge of the area.
The Eredivisie giants didn't waste any time to double their lead as Toivonen made it two only minutes later. Dries Mertens found the attacking midfielder with a low pass from the left, and the Swede controlled the ball before calmly slotting home.
The guests continued to dominate despite being two goals to the good, but sloppy defending from Timothy Derijck helped Trabzonspor back into the game.
The Belgian centre-back lost possession to Olcan Adin, who then dribbled past two opponents before finding the net with a delicate chip with the outside of his left boot.
Matavz seemed to restore his side's two-goal lead in the closing stages of the first half, but his goal was disallowed after he was adjudged to have handled the ball before slotting home. The former Groningen star again tried his luck after the break, but his low shot was easily collected by Tolga Zengin.
Inevitably, Burak continued to be Trabzonspor's main attacking threat, and the prolific hitman came close to levelling the scoring in the 55th minute, only to see Isaksson pull off a superb save, while another dangerous shot from the striker shortly after whistled inches past the post.
PSV almost made it three toward the end of the match when the referee awarded them a spot kick at the edge of the area. Toivonen stepped up to take it, but his curled shot went just wide of the post.
The second leg at the Philips Stadium takes place on February 23, with the Dutch side strong favourites to progress into the last 16 of the competition.