Zheng, 21, saved four set points on her own serve at 2-5 before Sabalenka wrapped up the set with a service winner after 33 minutes.
Zheng had hit a tournament-leading 48 in her six matches to reach the final but her serve let her down tonight.
Needing a strong start to the second set, she sent down three double faults in her opening service game to be broken again. She held after the political protest to trail 1-2 but won only one more game.
Zheng saved four match points – the third with a brave drop shot – before Sabalenka took her fifth with a forehand winner.