Three-time champion Nadal hastily opened accounts at the tournament with a 6-3, 6-2, 6-2 victory over Australia's John Millman on Tuesday at Arthur Ashe Stadium. The Spaniard improved to 15-0 in first round matches in New York and 42-6 on the season with the triumph.
"I'm very happy with the victory and very happy to be back in New York," said Nadal after his win. "The first match is always a little bit new. Even if I've played here many times, the beginnings are not easy. The serve worked well tonight and while my backhand wasn't as good as it can be, I am very happy."
Nadal will next face another Australian Thanasi Kokkinakis who battled past Belarus' Ilya Ivashka 6-3, 7-6(8), 6-7(4), 6-2 in three hours and 48 minutes.
"He has a big forehand, big serve," Nadal said of the 23-year-old wild card. "He's a dangerous opponent, of course. I need to go on court and play well."
Meanwhile, in women's singles, defending champion Osaka overcame the second set slump to take down the unseeded Anna Blinkova of Russia in three sets and advanced into the second round of the tournament.
The victory didn't come easily, however, as the top seed had to dig deep to claim victory at 6-4, 6-7 (5), 6-2.
The Japanese will next face Poland's Magda Linette, who lifted her first career WTA trophy at the Bronx Open last weekend. Linette defeated Astra Sharma of Australia 6-3, 6-4 to advance to set up clash against Osaka.