Marco Aurelio Motta's side pushed reigning champions Brazil all the way on Saturday before then falling short against China, but got it right for long enough today.
Serbia were unable to make their size count against their opponents, with Brankica Mihajlovic top-scoring with just 10 points - nine of them spikes.
Neslihan Darnel and Gozde Sonsirma both picked up 14 points for Turkey, who found huge success on their serve, sending down eight unreturned deliveries compared to none from their opponents.
Turkey next face South Korea while Serbia, who are effectively out of the running for a last-eight berth now, face the USA.
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