The Sparta Prague midfielder latched onto a low cross from Pavel Kaderabek two minutes before the hour and fired beyond Tolga Zengin from 12 yards to give the visitors a Group A triumph in Istanbul.
Turkey started the match well and moved ahead in the eighth minute through Umut Bulut, but they were unable to turn further possession into goals and were ultimately punished.
Tomas Sivok levelled with a powerful header eight minutes after Bulut's opener, but the Czechs had to wait until the second half for Dockal to seal the win.
With Iceland emerging 3-0 victors in Latvia, the Czech Republic remain second in Group A with maximum points from their two matches, while Turkey are bottom after a second straight defeat.
A slow start to the match from the visitors was punished inside the first 10 minutes as Turkey, who controlled possession in the early exchanges, took the lead through Bulut.
The Galatasaray striker timed his run perfectly to escape the attentions of the Czech defence, before placing a flicked header into the top corner, giving Petr Cech no chance.
Bulut nearly created a second for Olcay Sahan three minutes later but, after a neat interchange between the pair, the latter blazed his effort over the crossbar.
Pavel Vrba's side had posed little in the way of attacking threat, although a marauding run from David Limbersky sparked them into life.
The full-back's charge down the left saw him find Tomas Rosicky in the penalty area, but the Arsenal midfielder's effort was blocked by Semih Kaya.
From the resulting corner, though, Sivok rose clear of four defenders to bring the Czech Republic level.
Gokhan Tore and captain Arda Turan both wasted good chances to give Turkey the lead again as they posed more of an attacking threat, while Bulut saw a low shot well saved by Cech just before the break.
Having withstood pressure during the first half, the visitors came out with renewed attacking intent after the break and went close to moving ahead when Vladimir Darida fired a volley wide.
They did not have to wait long for a second goal, though, as Dockal capped a flowing move with a low finish from Kaderabek's cross after 58 minutes.
As tension grew inside the Sukru Saracoglu Stadium, the hosts battled in vain to find an equaliser.
Turan was beginning to have more and more involvement in proceedings but he was denied by Cech on two occasions just after the hour.
With time running out, Caner Erkin also had a chance to test the goalkeeper, but once again the 32-year-old Cech was more than equal to it to secure his side the win.
