Neither Kartal nor Bouzkova began with fluency, with the Briton broken in the first service game of the match.
Kartal could not convert a break back point in the next game and quickly found herself 4-0 down before she finally held serve.
Bouzkova, a talented doubles player, dictated the action and a double fault from Kartal handed her the first set.
The second set was topsy-turvy, with the players exchanging six breaks of serve before Bouzkova finally held for 5-4.
Kartal, 23, showed good grit in her final service game, saving four match points before Bouzkova finally converted.
