The Olympic gold medalist and 7th seed fired off eight aces and seized five break points on the Grandstand hard court in her first straight-sets victory of the year's final major.
Niemeier, nursing a foot injury, committed five double faults and held serve in just three games of the match that wrapped up quickly in an hour and 21 minutes.
Zheng was sharp from the start, blasting two aces to open the second game and breaking Niemeier's serve in the fifth to seize control of the match and energize scores of Chinese chanting 'jiayou' from the stands.
A cross-court forehand blast captured a second service break for the 2024 Australian Open runner-up as Niemeier's forehand return found the net.
Zheng grabbed seven straight points to open the second set and cruised to the win, avenging a third-round loss to the German at her first US Open in 2022 and setting up a fourth-round clash with either Donna Vekic or Peyton Stearns, who play later on Friday.
"Finally, it's the first match I won in two sets... It's not (been) easy for me to play after the Olympic Games," said Zheng, who has noted previous struggles with focus after deep tournament runs.
"I'm starting to find my tennis and I start to play better and better."
The enthusiastic support from Chinese fans also helped.
"Jiayou, means 'come on' in English... In Chinese, saying 'jiayou' to me, I feel a lot of energy and I feel it really brings me up."