Kvitova, a two-time Wimbledon champion and a three-time champion in New Haven, is just 4-4 on hard courts this season. The Czech player returned to the tour at the French Open in May after she was stabbed during a home invasion in December, leaving her dominant left hand seriously injured.
Zhang, ranked 29th, was playing her first match in the United States since April.
"I just arrived in New Haven last night, coming straight from China," she said. "It's a big change. It's 12 hours' time difference. Before the match I was still sleeping."
Bouchard, who reached a career-best No. 5 in the rankings in 2014, has struggled recently, slipping to 74th.
In other matches, Kirsten Flipkens of Belgium beat Lesia Tsurenko of Ukraine 6-2, 6-3, and Romania's Ana Bogdan got past Russia's Elena Vesnina, 7-5, 7-5.
The U.S. Open begins Aug. 28.
Disclaimer: No Business Standard Journalist was involved in creation of this content