"It was a really good fight between us," Sabalenka told reporters after firing 37 winners and committing 39 unforced errors.
"This was a match that I really enjoyed. She fights for every point, and it’s always so special when you feel this fight on court."
Broken early, Sabalenka won four games in a row en route to a 5-2 lead in the first set when Zhang staged a comeback to level it at 5-5 before the Belarusian clinched the set.
Sabalenka was more in control in the second set when she claimed a decisive break at 4-3 before serving out to set up a quarter-final clash with fifth seed Lesia Tsurenko of Ukraine.
"It's always special when you beat two good players in a row in the same tournament," Sabalenka said.
"It gives me more confidence. You finish the match and you really just think, 'When is the next one? I want to go back on court, I want to beat someone.'"
Briton Watson had little difficulty in beating Australian Fourlis, a victory which moves the 2015 champion into a quarter-final against Donna Vekic, and Alison Riske also advanced after Belgian qualifier Kirsten Flipkens pulled out with a right shoulder injury.
(Reporting by Amlan Chakraborty in New Delhi; editing by Peter Rutherford)
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