Australian Open champion Sabalenka – who will take over as world No 1 next week – booked her place in the last four with a 6-1, 6-4 victory in 1hr 13min.
The Belarusian second seed will face either Marketa Vondrousova of the Czech Republic or Madison Keys of the United States in the last four.
"I think I definitely played great tennis today," Sabalenka said, before praising her opponent.
"I'm super happy with the win against her, she played incredible tennis at the US Open this year."
Sabalenka was assured of replacing Iga Swiatek at the top of the women's rankings after the Polish No 1 crashed out of the US Open on Sunday.
However Sabalenka said she is not thinking about her new-found status as the world's top player just yet.
"Of course I'm happy ... it's incredible for me and my family.
"But I have some things still to do in New York this year and I'll think about becoming No 1 after the US Open."
Rising Chinese star Zheng had been dreaming of pulling off another upset after reaching her first Grand Slam quarterfinal by downing last year's finalist Ons Jabeur in the fourth round.
But the 20-year-old 23rd seed never looked like toppling the hard-hitting Sabalenka, who threatened to run away with the match after a blistering start in which she broke Zheng twice for a 3-0 lead, conceding just two points.
Zheng was broken again to go 4-0 down and although she finally held in the sixth game to make it 5-1, Sabalenka served out easily to take the first set in just 27 minutes.
Sabalenka's dominance was reflected in her serve, where she won 23 of 26 points on her first serve, and 13 of 19 on her second. Zheng was unable to open up a single break point opportunity across the match.
Zheng fared slightly better in the second set, but after Sabalenka broke in the seventh game for a 4-3 lead, the result was never in doubt, and she wrapped up victory on serve in the 10th game.
