The Serbian player, a two-time champion at Roland Garros, defeated Kovacevic 6-3, 6-2, 7-6 (7-1) on Monday.
Djokovic comfortably sailed through the first two sets, but encountered some resistance from the 24-year-old American in the third set.
Despite Kovacevic’s effort, his lack of experience became evident during the tie-break on the renowned clay court.
The match concluded with Djokovic clinching victory on his first match point, thanks to a scintillating service return.
Djokovic will next face Hungarian Marton Fucsovics as he vies for a place in the third round of the tournament.
“It’s always a pleasure to come back here, one of the best tournaments in the world,” said Djokovic, who made his Roland Garros debut in 2005.
“I’m very motivated to go far here, all the way I hope.”
Despite not having an ideal build-up to the clay-court Grand Slam, Djokovic displayed good form during the tournament, particularly in windy conditions.
He missed the Madrid Masters and was eliminated in the quarterfinals of the Rome Masters leading up to the French Open.
However, Djokovic managed to adapt well to the challenging wind conditions and showcased his skill and composure on the court.
His ability to perform at a high level despite the less-than-ideal preparation demonstrates his resilience and adaptability as a top-ranked player in the world of tennis.
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