The home side had the lead on 18 minutes when Jon Dadi Bodvarsson found the net on 18 minutes to claim his first-ever international goal.
The 22-year-old had the ball in the net after he nodded home at the back post after the ball floated over the goalkeeper.
The visiting Turks were forced to play the last half-hour with 10 men after Omer Toprak was given his second booking for handball.
With just under 15 minutes of normal time remaining, Tottenham Hotspur midfielder Gylfi Sigurdsson made it 2-0.
Moments later it was 3-0 when Ajax striker Kolbeinn Sigthorsson netted to give the home side a convincing win in Group A.