The fifth-ranked Zverev made a poor start to the clay season and crashed out in his opening match in Rome last week, and the German was in danger of throwing the title away against Jarry after taking the opening set.
A 90-minute rain delay interrupted play and Jarry twice had championship point in a final set tie-break before Zverev prevailed 6-3, 3-6, 7-6 (10/8) to earn his first title of the season.
"It was a very tough match. He was playing aggressively, serving big and hitting everything he can," Zverev told the ATP website.
"I thought I was in control until the rain came, but I'm happy to find a way. I felt it could have gone either way."
Zverev, who has never got past the quarter-finals of a Grand Slam tournament, will open his Roland Garros campaign against Australian John Millman next week.
"When I start playing good, I don't worry about titles. I know that I can be one of the best players in the world when I find my rhythm," said Zverev. "This week definitely helped with that."