Jonathan Walters' second-half goal was not enough for the home side as Fatih Terim's men secured victory in Dublin.
The two sides produced a frenetic start in front of a sparse crowd at the Aviva Stadium in Dublin and, although Ireland fell behind after just 17 minutes, O'Neill's men showed glimpses of what they were capable of.
Ahmet Ilhan Ozek broke the deadlock for the visitors, sending a bullet header beyond debutant Rob Elliot before the hosts took control, forcing Onur Kivrak into a string of impressive saves.
Turkey ultimately doubled its lead with 15 minutes to go, as Tarik Camdal found the roof of the net, but Jonathan Walters pulled one back a few moments later to ensure an intriguing finish.
Ireland made a lackluster start and allowed Turkey two chances inside the first minute. Mevlut Erding tested Elliot from distance, before Ozek sent a flicked effort over the crossbar.
The tie's blistering start continued, and Ireland appeared unlucky not to be awarded a fourth-minute penalty as Omer Toprak went unpunished after clumsily bringing down Shane Long inside the area.
Ireland were gradually growing in stature, and Kivrak brilliantly saved a header from Long in the 14th minute before John O'Shea's rebound was cleared off the line by Caner Erkin.
Turkey made the most of that let-off and took the lead three minutes later, as Ozek diverted Gokhan Gonul's right-wing cross into the bottom-right corner with a precise header.
Terim's side continued to look dangerous in attack, but susceptible at the back as the first half progressed.
The visitors' fullbacks were continuously targeted by Ireland and Kivrak pulled off another fine stop to deny James McClean in the 36th minute, after Aiden McGeady had glided past Gonul to send in a cross.
Proceedings were significantly more disjointed after the break, with halftime seemingly affecting Ireland's free-flowing football from the first half.
Nevertheless, the Irish continued to be the brighter side going forward, with the visitors' only real threat proving to be Hakan Calhanoglu, but Elliot confidently plucked the Hamburg man's deliveries out of the air on more than one occasion.
Turkey thought they had put the match beyond any doubt in the 75th minute as Camdal received Oguzhan Ozyakup's clever reverse pass before blasting past Elliot, but Walters registered with an emphatic finish on the counter three minutes later.
Terim's Turkey held on to the narrow victory and they continues it work against Honduras and the United States in the next two weeks, while Ireland faces tricky tests against Italy, Costa Rica and Portugal.