Peer edged Zheng 6-2, 2-6, 6-3 for her sixth career WTA title, surviving a 2 1/2-hour marathon match. Peer dropped her serve twice in each set but broke Zheng's serve all four times she served in the first set and three of four times in the third.
Peer won 57 percent of the points off Zheng's serve even though Zheng lost only seven points serving and saved three break points in the second set.
Zheng, 19 years old and No. 195 in the rankings, opened her tournament with a win over eighth-seeded Alize Lim and added victories over No. 4-seeded Zhang Shuai in the quarterfinals and second-seeded Misaki Doi in the semis in earning her first WTA title match appearance.
Peer took out top-seeded Timea Babos in the semifinals in earning a spot in a WTA final for the second time in two weeks. She was runner-up July 28 to Elina Svitolina at the Baku Cup in Azerbaijan. The win in Suzhou was Peer's sixth championship overall but first since September 2009.
Peer earned $20,000 along with the title, giving her about $4.7 million in career winnings. The second-place check for $11,000 pushed Zheng's career total to nearly $300,000.