The 27-year-old defeated 20th-seeded Evans in three sets, giving him his first win at Roland Garros since 2015 when he was still a teen.
For the second round, he will meet whoever wins between Stan Wawrinka and Albert-Ramos Vinolas.
Kokkinakis did admit that he was in a tough draw. In order to make it to the finals, he will have to take down some of the biggest names in Tennis today including possibly Andrey Rublev, Novak Djokovic, and Carlos Alcaraz.
“Someone sent me my path to the final, obviously ambitious, but it’s one of the toughest draws I’ve ever seen,” said Kokkinakis.
“But I probably wasn’t expected to win today either so I’ll rest up, recover and see what I can do.”
Kokkinakis had a brilliant career as a young player but he has since been plagued with injuries. Last season was the first time he was in the main draw of a Grand Slam since 2015.
“When it feels like half of your career has been kind of taken away, you hope you can have a bit at the back end,” Kokkinakis said.
“As long as my body is able to… we’ll see. There was a point when we didn’t think I’d play that much longer and I was 22 years old. I’m 27 now and who knows? Winning is addictive and losing makes you want to quit tennis.”
He does admit that he won’t be playing well into his 30s just to make up for lost time.
“I know I can’t do this forever. Whatever I do choose, I try not to take it for granted… I know where I was many years ago when I was missing out and not having opportunities.”
“You never know but I find it hard to see myself playing like these guys you see playing past 35, 36. There’s so much travel, from Australia constantly. Your social life pretty much goes out the window.”