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.
"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.