The 18-year-old made short work of the fifth seed and reigning Wimbledon champion, who was bidding to complete a career Grand Slam at Roland Garros, winning 6-4, 6-2.
Playing in the main draw of the tournament for the first time in her young career, Potapova claimed her first-ever victory over a top-10 player to set up a second-round tie against either fellow teenager Marketa Vondrousova or China's Wang Yafan.
"I was just speechless," she said. "I didn't know what to say and what to do, but, yes, I was so happy at that moment, and I'm still so happy.
"I live for this win, for these emotions, for these moments. I'm going to do everything to live it through again and again and again."
Potapova hammered 28 winners past the flailing Kerber, who had been struggling with a right ankle injury in the build-up to the event.
The Russian said she had looked up to Kerber, 13 years her senior, as a child.
"I was really looking forward for this match, because Kerber, I like her very much. She's actually one of my idols, and when I was young I was looking for her game, how she's playing," said Potapova, the 2016 junior Wimbledon champion.
"When you step in on the court and you know you play your, I would say idol, you've just got to show your best. That helped me. So, yeah, I was fighting for every point."
Potapova is one of several teenagers making their presence felt on the WTA Tour this year.
Czech Vondrousova claimed a surprise win over reigning French Open champion Simona Halep last week in Rome, while 17-year-old American Amanda Anisimova reached the Australian Open last 16 and Canada's Bianca Andreescu, 18, was a shock title winner at Indian Wells.
Potapova admitted that the attention that comes with winning such a big match on Court Philippe Chatrier was something new.
"My phone is exploding right now, you know, social media, anything, WhatsApp, the messengers."
The draw could open up nicely for Potapova, too, with 28th seed Carla Suarez Navarro the highest-ranked player she can face before the fourth round.
French Open results on Sunday, the first day of the 2019 tournament (x denotes seeded player):
Stefanos Tsitsipas (GRE x6) bt Maximilian Marterer (GER) 6-2, 6-2, 7-6 (7/4)
Marin Cilic (CRO x11) bt Thomas Fabbiano (ITA) 6-3, 7-5, 6-1
Matteo Berrettini (ITA x29) bt Pablo Andújar (ESP) 6-7 (3/7), 6-4, 6-4, 6-2
Casper Ruud (NOR) bt Ernests Gulbis (LAT) 6-2, 7-6 (7/2), 6-0
Oscar Otte (GER) bt Malek Jaziri (TUN) 6-3, 6-1, 4-6, 6-0
Alexei Popyrin (AUS) bt Ugo Humbert (FRA) 3-6, 6-3, 7-6 (12/10), 6-3
Garbine Muguruza (ESP x19) bt Taylor Townsend (USA) 5-7, 6-2, 6-2
Johanna Larsson (SWE) bt Magdalena Rybarikova (SVK) 6-3, 6-4
Anastasia Potapova (RUS) bt Angelique Kerber (GER x5) 6-4, 6-2
Petra Martic (CRO x31) bt Ons Jabeur (TUN) 6-1, 6-2