The 39-year-old trailed twice by a break in the opening set, eventually winning in a tie break before decisively sweeping aside 28-year-old Ahn.
It took Williams one hour and 41 minutes to eventually surpass Ahn 7-6 (7-3), 6-0 and advance to the second round at Roland Garros.
“The biggest difference was just confidence,” the No.6 seed said afterwards. “I just need to play with more confidence, like I’m Serena.
“So that was it. I just started playing like that, and I love the clay and I started playing like it, opening the court and moving and sliding.”
Williams is aiming to tie Margaret Court’s Grand Slam win total of 24. She is just one away with 23.
She came close to equaling the record at the US Open last month, eventually losing in the semifinals to Victoria Azarenka.
Williams has won the French Open three times, the last victory coming in 2015. She lost in the final a year later to Spaniard Garbiñe Muguruza.
In the second meeting between the pair in the space of a few weeks — Williams beat Ahn in the first round of the US Open — it was the world No.101 who started the fastest.
Having not played on clay since losing to Sofia Kenin in the third round at Roland Garros in May 2019, Williams looked rusty which allowed Ahn to capitalize and race into a 4-2 lead in the opening set.
Williams battled back though, tying the score at 4-4 and after going to a tie-break, clinching the opening set with her seventh ace.
And after getting warmed up, the former world No.1 quickly raced to victory, breaking Ahn’s serve three times in a row and winning the match with her 11th and final ace of the game.
“I have to let go of that expectations. That doesn’t mean I’m lowering my expectations,” Williams said. “It just means I’m having realistic expectations of not winning every point, every game, every shot.
“It sounds crazy, but, you know, that’s me and that’s what makes me me. I’m me. I’m Serena. At some point I’m always going to have some level of perfection, but I just need to have a more reasonable level so I cannot put so much stress on me mentally.”
Williams will play Bulgaria’s US Open quarterfinalist Tsvetana Pironkova in the second round.