Under pressure to avoid defeat with Netherlands chasing third spot, Turkey earned the win with a late strike as their Dutch rivals slipped to a 3-2 defeat against Czech Republic.
The win proved to be enough for Turkey to qualify as they claimed a spot as the best third-placed side in the qualifying groups.
It was the hosts who started the better in the early stages of the game, and they came agonisingly close to claiming the advantage when Oguzhan Ozyakup's effort from the edge of the box drifted just past the post.
Despite improving as the game progressed, Iceland looked vulnerable at the back and were left breathing another sigh of relief after Volkan Sen fired wide when Hakan Calhanoglu's free kick caused problems for the visitors.
Turkey continued to dictate the tempo either side of the interval, but they were sent a warning by Iceland when Gylfi Sigurdsson fired just over from long range.
The score in the crucial game in Amsterdam may have allowed the home fans to relax, but the nerves on the pitch were clear as Iceland started to find more space, with Kolbeinn Sigthorsson heading just wide of the post.
However, their task was made more difficult heading into the closing stages thanks to a moment of madness from Gokhan Tore, who was shown a straight red card for a dangerous tackle on Jon Dadi Bodvarsson.
There would be a late twist as the 10 men clinched all three points when Inan stepped up to curl home a stunning free kick to earn his side a place at next summer's tournament.