Burak Yilmaz raised spirits among the home fans when he headed Turkey ahead in the 62nd minute from an Arda Turan cross but their joy was short-lived as substitute Daniel Bode pounced on a defensive error to equalise nine minutes later.
Turkey moved up to seven points and remain fourth in the group, which is headed by 2010 World Cup runners-up Netherlands. Hungary are on 11 points.
Turkey, who are looking to qualify for the World Cup for the first time since finishing third in the 2002 tournament, and Hungary both wasted numerous chances to score until the hosts broke the deadlock.
Turkey's Alper Potuk shot wide in the 22nd minute while Hungary defender Vilmos Vanczak was unlucky to miss two scoring opportunities as he had a header saved by goalkeeper Onur Recep Kivrak and then hit the post.