Turan's low shot in the 78th minute deflected off a Belgium defender into the bottom corner of the net.
Daniel Van Buyten had put Belgium ahead in the 28th minute, heading in a corner from Toby Alderweireld.
Hamit Altıntop leveled the score in the 47th minute before substitute Semih Senturk gave the hosts the lead in the 66th, two minutes after Belgium defender Vincent Kompany had been sent off for a second booking.
However, Belgium responded just three minutes later when goalkeeper Onur Kivrak left his line late on a cross, leaving Van Buyten to head in his second.
"With the corner, we got caught and that was a blow to the team," Turkey coach Guus Hiddink said. "I like to have some options (for the second half) and luckily it worked very well."
Belgium next head to Kazakhstan in search of its first win, while Turkey will look to maintain its perfect record at Germany.
Lineups:
Belgium: Logan Bailly, Toby Alderweireld, Daniel Van Buyten, Vincent Kompany, Thomas Vermaelen, Timmy Simons, Guillaume Gillet, Jan Vertonghen, Romelu Lukaku, Marouane Fellaini, Moussa Dembele (Kevin Mirallas, 62).
Turkey: Onur Kıvrak, Servet Çetin, İsmail Köybaşı, Emre Belözoğlu, Hamit Altıntop, Tuncay Şanlı, Arda Turan, Mehmet Aurelio, Ömer Erdoğan, Selçuk İnan (Semih Şentürk, 71), Sabri Sarıoğlu (Gökhan Gönül, 73)
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