The unseeded 24-year-old won 6-4 6-1 to become the first British woman to reach a Grand Slam semi-final since Jo Durie made the US Open last four in 1983.
Konta, ranked 47th, will next face German seventh seed Angelique Kerber.
Fellow Briton Andy Murray takes on Spain's David Ferrer in the men's quarter-finals later on Wednesday.
"I didn't put anything on this match," said Konta. "I just wanted to come out and play the best level that I could, and give the best entertainment I could."
The British number one took full advantage of facing a quarter-final opponent who was also in uncharted waters, seeing off world number 133 Zhang in one hour and 22 minutes.
Konta began confidently, breaking twice and serving superbly as she moved 5-2 clear before overcoming some nerves and a resurgent opponent to clinch the set.
After saving a break point that would have made it 5-5 and then converting her sixth set point, the confidence returned and Konta again earned a double-break lead in the second set.
With a Grand Slam semi-final place there for the taking, Konta saw two match points slip by but converted the third thanks to a net cord that left Zhang helpless.
"To be honest, I was taking it a match at the time. She definitely didn't make it easy for me," said Konta.
"Every time I was ahead she was constantly there. I'm not proud of the net cord but I'm happy I was able to fight every point."
The latest step in Konta's stunning rise through the tennis ranks brings with it a likely position among the world's top 30, and guaranteed prize money of at least £370,000.
A Grand Slam final appearance is now a real possibility, arguably more so after Kerber's surprise win over the in-form Victoria Azarenka earlier on Wednesday.
Kerber and Konta will meet for the first time in Thursday's second semi-final at around 04:30 GMT.
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