Nadal's physical state is always a concern but the Spaniard looked sharp in a 6-3 6-2 6-2 victory.

The second seed broke Millman's serve five times in a one-sided match.

Nadal, 33, will play Millman's fellow Australian Thanasi Kokkinakis in the second round.

Kokkinakis, 23, has seen his career disrupted by a serious shoulder injury and will face the 18-time Grand Slam champion after earning his first win at a major since the 2015 French Open.

Nadal is no stranger to injuries himself, of course, and his comfortable win against Millman was a happy return to Ashe, where he was forced to retire from his semi-final against Juan Martin del Potro with a knee problem last year.

Returning to deafening cheers for Tuesday's night session, Nadal made a customary slow start as he fought off a break point in the first game before taking 30-year-old Millman's serve in the fourth proved enough for the opener.

Millman, ranked 60th, earned the biggest win of his career against Federer in last year's last-16 match after fighting back from a set down.

But he was unable to produce a similar fightback with Nadal focused and firing on the other side of the net to clinch victory in two hours and 11 minutes.

Australia's Nick Kyrgios reached the second round at Flushing Meadows by defeating American Steve Johnson 6-3 7-6 (7-1) 6-4 in the late match.

Kyrgios, seeded 28th, fired 24 aces on the way to his victory and will face French wildcard Antoine Hoang next.

"I knew I had to play top-flight tennis," Kyrgios said. "I had to serve well. I'm happy to get through."