World number one Novak Djokovic, 35, continued his red-hot form at Roland Garros with a straight-sets win over victory over Alex Molcan. The defending champions defeated 24-year-old Slovakian at 6-2, 6-3, 7-6 (4) at Court Suzanne Lenglen.
Molcan did push the 20-time Grand Slam champion to a third-set tiebreaker in Paris but failed to make it count.
Djokovic will next face 32-year-old Slovenian Aljaz Bedene, who defeated Pablo Cuevas of Uruguay in four sets, 4-5, 6-4, 7-5 (5), 6-4.
But Carlos Alcaraz endured a five-setter against 44th-ranked Albert Ramos-Vinolas. The 19-year-old Spaniard saved a match point in the fourth set and then was forced to fight back in the decider to win his second-round match 6-1, 6-7 (7), 5-7, 7-6 (2), 6-4.
In a match that lasted more than four and half hours, the sixth-seeded Alcaraz won six of the final seven games to settle a nervy match against his fellow Spaniard at Court Simonne-Mathieu.
Earlier, Alcaraz became the first man to beat both Nadal and Djokovic in the same tournament on clay. He then went on to win Madrid Open.
Alcaraz next face Sebastian Korda. The 27th-seeded American defeated French veteran Richard Gasquet in straight sets, 7-6(5), 6-3, 6-3.