Sabalenka, who will move top of the world rankings next week, pummelled her Chinese opponent with 17 winners and never faced a break point.
Zheng had never made it to a major quarter-final and endured a miserable time against the Australian Open winner, as she was unable to get much power off her serve and the Belarusian forced her into 23 errors.
Sabalenka will play the winner of a match between American Madison Keys and Wimbledon champion Marketa Vondrousova.
"I'm super happy with the win against her... super happy with the performance," said Sabalenka, who lost in the semi-finals in her previous two US Open appearances.
"I'm going to do everything I can to stay until the end."
Sabalenka has not dropped a set this year at Flushing Meadows and she won the first five games, dropping only one first-serve point in a near-pristine first set.
Zheng improved in the second set, forcing Sabalenka to run back and forth along the baseline as she showed finesse to triumph in a 21-shot rally in the fifth game.
"In the second set, she start playing better, serving better. I kind of expect that, because after first set it was, like, nothing to lose for her, she start playing a little bit more aggressive," Sabalenka said.
Zheng helped Sabalenka to her break with a double fault and two unforced errors in the seventh game and never recovered, sending a backhand into the net on match point to prompt a satisfied fist-pump from her opponent.
"It was a little tricky, and I'm super happy that even though she was serving really well, I was able to break her serve for once, and it was enough for that set," Sabalenka told reporters.
"I'm super happy that even though she tried to play more aggressive, I was able to keep my level."
Zheng said she would learn lessons from the loss.
"I feel against her I need to know how to (defend) better and stay more in the rally," she told reporters.
"Sabalenka, she's a tough opponent to beat, and the loss today made me think a lot."
