Turkey grabbed the lead in the eighth minute when Caner Erkin swung in a deep cross from the left and Umut Bulut headed the ball past keeper Petr Cech.
The visitors levelled seven minutes later as Sivok outjumped his markers to nod in a corner from Ladislav Krejci.
Turkey were then made to pay for missing several good chances when Dockal fired a left-foot shot beyond home keeper Tolga Zengin in the 58th minute.
The Czechs are joint top of the table with six points from two matches while Turkey are bottom without a point.
Iceland also have six points after beating Latvia 3-0 on Friday.
"If somebody had told me we would have six points at this stage I would have said they were crazy," said Czech coach Pavel Vrba.
Turkey were especially wasteful in front of goal in the first half and failed to find the cutting edge that would have made the most of their possession.
Gokhan Tore dragged a shot just wide from inside the penalty area while Arda Turan's long-range effort flew over the bar in the opening period.
Erkin also went close just before the break when his free kick hit the outside of the post.
"We survived many situations in the first half and were lucky," said Vrba. "The second half was much better, we didn't lose the ball so easily."
(Writing by Michael Kahn, editing by Tony Jimenez)
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