The Japanese player came from a set down to beat the American teenager in her second-round clash at the Western & Southern Open.
World No.1 Barty fought back from a break down in the second set to reach her first Wimbledon final where she will face Karolina Pliskova.
World No.25 and former Wimbledon champion Angelique Kerber defeated Karolina Muchova in Wimbledon quarterfinals. She will meet the winner of Ash Barty.
Zverev seemed on course for victory but the Canadian turned things around to everyone's shock in the final set.
Kerber came from a set down to ease her way into the fourth round. Elsewhere, Ajla Tomljanovic produced a upset win over Jelena Ostapenko.
Kerber seemed relieved after the match as she spoke about how much the victory meant to her, especially ahead of Wimbledon.
Round 1 of the French Open 2021 began on Sunday (May 30), and Japan's Naomi Osaka started the tournament with an easy win.
She had sustained a tear in her left calf during her recent Italian Open Round of 32 match against German player Angelique Kerber in Rome.
Kiki Bertens had claimed the Madrid title at the event's most recent edition in 2019.
The three-time champion Kvitova edges past the German to reach the third round in Madrid.