Sinner of Italy battled a hip issue leading up to Roland Garros, but he played brilliantly in a straightforward victory of 6-3 6-3 6-4.
Sinner was disturbed only over the final stretch of the match, giving his American opponent two break points via a double fault before rallying to win.
“My hip feels great, and I’m really happy,” the 22-year-old exclaimed.
“The general shape is not at 100% yet so we try to build every day.”
Rain delayed much of the day’s play, but Greek ninth seed Stefanos Tsitsipas prevailed as well on Monday, defeating Marton Fucsovics 7-6 (9-7) 6-4 6-1.
Additionally, Frenchman Gael Monfils and Russian fifth seed Daniil Medvedev also prevailed in the day two evening session.
Should defending champion Novak Djokovic fall short of the semifinals, Sinner will rise to the top of the world rankings in Paris.
Against Eubanks, he performed admirably, scoring 33 winners and saving nine of the ten break opportunities he faced.
Next up for him is local favorite Richard Gasquet.
“I’m pleased with the progress I’ve made in recent months. Daily improvement is the aim, he continued.
