The visitors struck twice in the first half, and despite Omer Toprak's late strike, the hosts were unable to come away from the contest with a positive result
Despite commanding the lion's share of possession, the Turks lacked a sense of incisiveness, and first-half goals from Vladimir Weiss and Miroslav Stoch ensured the Slovakians returned home with a credible away win.
The warning signs were there for Turkey from the very start. Marek Hamsik charged down the right within moments of kick-off, only to see his cross blocked by Semih Kaya.
Some slack defending allowed Stoch a shot on goal, but thankfully for the hosts, the Fenerbahce man's long-distance drive sailed comfortably wide.
Sinan Bolat was called into action soon afterwards, producing an excellent save after a snap-shot from Marek Bakos. The Standard Liege stopper was well-placed once more minutes later, after Semih Kaya deflected Stoch's cross towards his own goal.
Gradually, however, the hosts began to craft chances. Nuri Sahin blasted a strike narrowly off target from distance, before Mustafa Pektemek's shot found the side-netting after some good work from Mehmet Ekici.
Sahin had a shot blocked within the box, before the deadlock was finally broken. Weiss collected the ball on the right wing, and dribbled past the static Turkish defence before placing the ball beyond Bolat, who, truth be told, could have done far better with the tame shot.
The hosts immediately set about trying to get back on level terms. Dusan Pernis did well to get his body behind a curling Sahin free-kick, then went on to make a great save from a deflected Olcan Adin effort.
The Dundee United 'keeper was going through a busy spell. A free-kick was deftly laid off to Mehmet Topal, whose powerful drive was well held on the line.
However, the pressure proved to be of little consequence. Stoch gathered the ball on the left-wing, cut inside and sent in a shot that a deflection carried over Bolat.
Slovakia came close to adding a third moments after the restart, with Hamsik sending a shot, that had a grateful Bolat scrambling across goal, wide.
However, the hosts soon went about trying to find a path back into the contest. Ekici blasted an effort high and wide from the edge of the box with his less-favoured left foot, before Burak Yilmaz, fresh from the bench, sent a header narrowly wide.
Arda Turan almost marked his first international appearance as captain with a goal, but his left-footed shot drifted agonisingly wide.
Omer Toprak had a shot blocked on the line, before the Bayer Leverkusen man finally found his nation a path back into the match.
Kaya nodded on a Tunay Torun corner at the near post, and Toprak was there at the far post to bundle the ball home.
Slovakia's two-goal advantage was almost restored minutes later, with Bolat acrobatically tipping Filip Holosko's effort over.
But the miss was to matter little. The first-half salvo was enough for the visitors to come away with an excellent, well-earned victory.