Roger Federer, Rafael Nadal and Kei Nishikori advanced to the quarterfinals on cue.
But Wawrinka, beaten by fellow Swiss Federer in the final of Indian Wells earlier this month, looked weary as he struggled through the third set of a match played on his 32nd birthday.
"I had one bad game to start the second set and then it was tough for me," said Wawrinka, the reigning US Open champion. "I don't know. I completely went down physically and mentally, and also my tennis was completely out. I had no more gas."
"For sure it's a disappointing match. I think the level was quite up and down. We were both fighting a little bit in the first set to find good level. It was really humid, not easy to play some great tennis," he added.
The 19-year-old Zverev saved four of five break points and won 75 per cent of his service points.
"I had to be aggressive. I felt like he was the one controlling all the points all the time, so I had to change that. It worked out well for me," Zverev said.
The German, seeded 16th, will now face Australian Nick Kyrgios, who was impressive in a 7-6 (7/5) 6-3 win over Belgian David Goffin.
Federer had to work hard for his victory against 14th seed Roberto Bautista Agut, emerging with a 7-6 (7/5) 7-6(7/4) win setting up a last eight meeting with Czech Tomas Berdych, the 10th seed, a 6-3, 7-5 winner over France's Adrian Mannarino.
"It was a different kind of match," said Federer, who is in an excellent run of form having won the Australian Open and Indian Wells already this year.
"It wasn't the big-serving match where you're only going to see so many looks, you know, so when you miss chances you always feel a bit frustrated sometimes.
"That's where you got to keep a positive mindset and make the right plays," he added.
The first set was a close and entertaining battle. Bautista broke to go 5-4 up but Federer then won every point in the next two games. The tie-break saw some fantastic tennis from both players but the Swiss delivered at the close.
"I thought Roberto did a good job of making shots, staying offensive when he could, fending off a lot of good shots that I hit," Federer said. "Then it was tough. The sun was coming from the side in the beginning so it's hard to chase the lines."