Handed a wildcard by organisers, the 17-year-old Frenchman looked entirely unfazed on Court Simonne Mathieu in the first-round match as he made his Grand Slam debut against a player 20 years his senior and a former world number three.
Cilic, the 2014 US Open champion and a Roland Garros semi-finalist in 2022, arrived in Paris ranked 46th in the world but was outplayed by the fearless teenager, whose speed in defence and deft drop shots repeatedly drew applause from the crowd.
Ranked 318th, Kouame edged a tense opening set in a tiebreak after saving two set points before taking control of the match.
"It wasn’t easy. I always try to stay in the present moment and not think too much about the score. Today I managed to do that really well," Kouame said on court.
Kouame did not concede a break of serve throughout the contest as he sealed victory in straight sets.
At 17 years and two months old, Kouame became the youngest player to win a Grand Slam match since Australia’s Bernard Tomic reached the 2009 Australian Open second round at the age of 16.
He is also the youngest player to advance past the first round at Roland Garros since Romania’s Dinu Pescariu achieved the feat in 1991 at 17 years and one month old.
"It’s a lot of emotion, it’s exceptional," Kouame said.
"Coming into this tournament, I didn’t really know what to expect. The team and I worked hard to be as ready as possible."
The teenager, coached by former French player Richard Gasquet, claimed only the second main-tour win of his career after earning his first at the Miami Masters in March.
He will next face Paraguay's Adolfo Daniel Vallejo, who advanced after 20th seed Cameron Norrie retired injured.
Kouame’s breakthrough run caps a rapid rise this season.
The Frenchman has won three ITF titles - the third tier of professional tennis - and received several wildcards on the main circuit, including at the Miami and Monte Carlo Masters.
"All the experience I gained in Miami and Monte Carlo probably helped me a little," Kouame told reporters.
"Technically, I felt pretty calm. I knew I was ready, and I felt good mentally and physically."