The visitors, surprisingly beaten at home by Romania on Friday, made it zero points from a possible six to sit well off the pace in Group D.
The night started well for Turkey as Mevlut Erdinc put them ahead midway through the first half, but Vladimir Koman levelled before the break. Adam Szalai put the hosts in front five minutes after half-time and Zoltan Gera added another from the penalty spot eight minutes later.
The Turks were expected to be the main challengers to group leaders the Netherlands, but after four games are nine points behind the Dutch and six behind Hungary and Romania. Hungary, by contrast, are up to second on goal difference.
Turkey went ahead in the 22nd minute as Caner Erkin's cross was fired low into the net from the centre of the area by Erdinc. The hosts were then level nine minutes later as Koman's low ball in from the left crept inside the near post.
Sandor Egervari's side were on top now in more ways than one and Koman shot wide and Zsolt Korcsmar headed just off target in quick succession. They had to wait just five minutes after the break to take the lead as Szalai swept home Tamas Kadar's cross from the left.