Hosts Turkey dominated proceedings early and took an eighth-minute lead in Istanbul, but they were ultimately punished for failing to take advantage of possession.
Tomas Sivok equalised eighth minutes later before Borek Dockal struck the winner in the 58th minute as Czech Republic maintained their unbeaten start in Group A.
Czech coach Pavel Vrba conceded post-match that his team were extremely lucky to leave Sukru Saracoglu Stadium with all three points.
"Me and my team are so happy about the result," Vrba said afterwards.
"We were so lucky, especially in the first half, because we couldn't get organised and Turkey had a lot of chances.
"We're so lucky that we didn't concede more than once. But in the second half we were better organised, we created more chances, and finally we scored.
"But if we had been better with our final ball, we could have scored three or four, though in the end it's such a good result away from home and we're happy about that."
Czech are joint leaders alongside Iceland in Group A, with two wins from two games.
Turkey languish at the foot of the standings, still searching for their first points but Vrba expects the Turks to be among the teams battling for second spot, with Netherlands tipped to top the group.
"Netherlands are still the big favourites in this group, and the fact Turkey have not got any points is not a big deal because they are always a very strong team and they can recover," he said.
"For me, three teams are chasing second place – ourselves, Turkey and Iceland.
"Getting these two wins on board is a big head start for us, but it is no guarantee of finishing second in this group."
Czech Republic travel to minnows Kazakhstan on Monday.
