Alcaraz, seeded second in this year's French Championships, got nothing for free against Zeppieri when he won in three sets, 6–3, 6–4, 6–2.
Norwegian Casper Ruud, who lost the finals in 2022 and 2023, had no trouble at all against another qualifier, Spaniard Albert Ramos-Vinolas.
Ruud had already shown with his victory in Madrid recently that he had prepared well for the second Grand Slam.
He reached the second round – where Portuguese Nuno Borges awaits – via 6–3, 6–4, 6–2.
World number one and top-seeded Jannik Sinner went in against home player Arthur Rinderknech. The Frenchman beat Sinner in Lyon years ago, but was now without a chance. This year's Australian Open winner Sinner, who recently returned after a three-month doping suspension, won with 6–4, 6–3, 7–5.
Fifth-seeded Pole Iga Swiatek, last year's winner, eliminated Slovakian Rebecca Sramkova with 6–3, 6–3.
On Tuesday, 24-time Grand Slam winner Novak Djokovic will enter the men's singles, and the women's singles has second-seeded American Coco Gauff as the main attraction.
