After a goalless draw in their debut FIFA-recognised game against Haiti in March, Kosovo came into Wednesday's friendly in Mitrovica looking to break new ground.
They managed that 10 minutes before half-time when already 2-0 down, Kaiserslauten forward Bunjaku slotting home after Turkey goalkeeper Volkan Babacan had spilled the ball at his feet.
Goals from Ahmet Ilhan Ozek and Bilal Kisa had put a youthful Turkey side in control before that, and the visitors pushed home their advantage after the break.
Half-time substitute Olcay Sahan rattled in a third, before Mustafa Pektemek claimed a brace and Alper Potuk added a sixth from the penalty spot with three minutes to go as Kosovo tired.
The hosts got off to a shocking start as they fell behind in the second minute.
After clearing a Kosovo corner, Turkey broke through Pektemek, who crossed from the left and, after a defensive slip, Ozek slammed home a finish from 14 yards.
Pektemek was brilliantly denied by Kosovo goalkeeper Kushtrim Mushica as the visitors poured forward, seeing his close-range effort tipped over the bar in the 18th minute.
The keeper was again called into action after shortly afterwards, flying high to his left to tip Tarik Camdal's dipping volley behind for a corner.
Kosovo's insistence on playing the ball out from the back was fraught with danger on a slow-looking surface and it proved costly as they conceded a second goal 11 minutes before the break.
The hosts surrendered possession deep in their own half, and Kisa unleashed a swerving left-footed shot from 30 yards that crept in off the right-hand post.
However, Kosovo pulled one back almost immediately to delight the home fans, Bunjaku tapping home into an empty net from four years after Babacan fumbled.
Fatih Terim introduced Sahan at half-time and the Besiktas man had an immediate impact, sending a searing strike in off the crossbar from 25 yards in the 49th minute.
A fourth followed five minutes later, Pektemek stabbing home from five yards after Mushica had parried Potuk's rasping drive from the edge of the box.
Pektemek was on target again on 71 minutes, heading into an empty net after being teed up by Sahan before Potuk had the final say on what was a historic day for Kosovo.
