The 16th seed equalled her best run at Flushing Meadows after a 6-2 6-3 victory.
Konta took just 54 minutes to dispatch Margarita Gasparyan in their rain-delayed second-round match on Thursday.
And the 28-year-old was in no mood to hang around again, beating Chinese 33rd seed Zhang in one hour and 12 minutes on the Grandstand court.
— WTA (@WTA) August 30, 2019
"They are never clean and straighforward matches, there's always two players on court ," she said.
"There was nothing easy about that match, I had to stay clear on what was happening in the match.
"I strongly believe in the process and progression and I'm constantly trying to grow and get better. I lost two first rounds before this tournament so I'm trying to keep things in perspective."
Konta will meet third seed Karolina Pliskova in the last 16.