With rain this week putting the pre-US Open event behind schedule, the winners were forced to compete twice in the day in hopes of getting the event finished on Monday, as planned due to the Paris Olympics.
Zverev, the 2017 champion in Canada, had a serious wobble at 4-all in the final set, giving up the game to Korda as the American took full advantage for a 7-6(5), 1-6, 6-4 upset of the world number four.
Australian Popyrin accounted for a second straight seed with his 3-6, 7-6(5), 7-5 fightback against one of the game's biggest servers in fourth seed Hubert Hurkacz.
Victory took nearly three hours, with his semi-final against Korda scheduled for the evening session.
In the third round, Popyrin had saved three match points in beating 10th seed Grigor Dimitrov.
Hurkacz had not lost to an Aussie since 2021 in Madrid. The Pole was playing this week less than a month after July knee surgery, with doctors telling him his season was over.
"I'm really happy but a little bit tired," Popyrin said after winning with 11 aces. "I have another match in about two hours."
Korda beat Popyrin in their only previous ATP meeting at Kazakhstan two years ago.
Korda is on a career-best win streak of eight straight matches. His victory over Zverev after more than two hours was only his second against a top-five opponent.
He will be competing in a Masters semi-final for the second time in his career.
"This means a lot to me. It has been a tough year," said last weekend's ATP Washington winner.
"I've put in a lot of work so I'm happy with the results. I'm having fun on the court and trying to play aggressive tennis."
The son of a former ATP champion from the 1990s has advanced with minimal play. His first-round opponent retired and he got a walkover in the third round when Casper Ruud fell ill.
"I wish I could have played more matches. But I'm feeling good and that's the most important," Korda said.
"I want as many matches as I can get," he added after notching his 30th win of the season.
