The British No. 1 has never won a match in Paris in four appearances in the main draw. She made 29 unforced errors in the first set.
Hers was not the only significant surprise of Day 1.
The Latvian stunned the world past year with a series of upsets before beating Simona Halep in the final but struggled for any sort of rhythmn today against her Ukrainian opponent.
The 21-year-old, who arrived at Roland Garros on a hot streak of form after titles in Munich and Madrid before an Italian Open final loss to Rafael Nadal, stormed to victory in only an hour and 10 minutes.
The seven-time Grand Slam champion is looking to reach the French Open quarter-finals for the first time since 2006 after back-to-back last-16 defeats. A native of Nikolaev from-for traumas has not appeared in court more than two months, but because her chances in the match against Ostapenko was seen at a very low level.
The second seed thrashed unseeded Lithuanian Ricardas Berankis 6-1, 6-1, 6-2 as he chases a first Grand Slam trophy.
Venus Williams crashed to a straight-sets defeat in the opening round, losing 6-4 7-5 to China's Qiang Wang on Court Suzanne-Lenglen.
Jelena Ostapenko leans into a return in the first round of the French Open on Sunday.
Two matches have been left unfinished at the French Open as play was suspended Sunday night due to darkness.
On a sunny and warm day, Stephens was joined in the second round by fourth-seeded Elina Svitolina, who defeated Ajla Tomljanovic 7-5, 6-3 after recovering from a 5-1 deficit in the opening set.
"I think today I had nothing to lose", added the 26-year-old, who is coached by former Wimbledon doubles champion Peter McNamara. "I try to do everything what's in my power to play my best game on the Grand Slams", she said.
She wound up with 48 unforced errors, more than twice as many as Kozlova, and that was more than enough to render Ostapenko's 22-13 edge in winners irrelevant.
Alize Cornet advanced in her homeland, while fellow seeds Barbora Strycova and Anett Kontaveit came through their opening matches.
Venus Williams and rain are on the schedule as the year's second Grand Slam tournament is set to start at Roland Garros. "I think her game just got better and better during the match".
The French Open is the only major tennis championship that begins on a Sunday, making it a 15-day event.
Other leading men were forced to work a lot harder in matches they would have been expected to breeze through: No. 2-seeded Alexander Zverev, No. 4 Grigor Dimitrov and No. 19 Kei Nishikori all faced two-sets-to-one deficits and all emerged to win Wednesday.