Wozniacki, who had received a bye into the second round, was beaten by Zheng's aggressive tactics with the Chinese hitting twice as many winners as the Dane (34 to 17).
Flyweight Yafai, who received a bye into the second round in Beijing, was always trailing and struggled to impose himself on the fight as he slipped to a 9-3 defeat.
The top seven seeds receive a bye into the second round and the world No. 5 Juan Martin Del Potro made hard work of his place in the third round after a battle with Ukrainian Alexandr Dolgopolov.