Seventh seed Zheng, a quarter-finalist in New York last year, won 73% of her first-serve points and converted six of her 11 break-point chances during a two hour 20-minute match at Louis Armstrong Stadium where she was broken four times.
"At the beginning I didn't have my first serve but the more the match goes I started to find my rhythm on the hard court," Zheng said during her on-court interview.
"In the second set I really believed all my shots helped a lot and I started to be more consistent and little by little I started to get more into the rhythm."
Anisimova raced out to a 5-1 double break lead in the first set but then had to dig deep as Zheng broke back at love, turned aside three set points on her next serve and then broke again to get the match back on serve.
But Anisimova, having twice failed to serve out the set, found another way as she broke a misfiring Zheng for a third time to grab the first frame.
In the second set, Zheng suddenly looked more comfortable from the line, including during a four-ace game to reach 2-2 before she broke in the next game to put Anisimova on the back foot and then leaned on her serve to close out the frame.
Zheng jumped out to a double break 3-0 lead in the decider while Anisimova, who had her left foot tended to before the set and at one point winced after a shot due to discomfort in her right hand, was unable to find her way back.
Up next for Zheng, who arrived in New York having played just two hardcourt matches since winning the Olympic singles gold medal on the Parisian clay at Roland Garros, will be a clash with Russia's Erika Andreeva.