The two-time Wimbledon champion is just the seventh player to reach the 850-win mark, joining Roger Federer, Jimmy Connors, Ivan Lendl, John McEnroe, Andre Agassi and Guillermo Villas.
With 217 Grand Slam match victories, Nadal is now in sixth place on the all-time list at the majors.
Nadal, seeded to face defending champion Andy Murray in the semi-finals, will play Donald Young for a place in the last 32 as he bids to win Wimbledon for the first time since 2010.
“I haven’t had many matches on grass for the last few years, but I had some positive feelings,” Nadal said.
“For all the players it’s so special to play here, especially for me with all the history I have here. It’s very emotional to be back.
“I’m happy with the way I started. I’ve been playing well since the beginning of the season.
“The clay-court season was special for me and now I have an opportunity to compete on grass.”
Having won the French Open without dropping a single set, Nadal has made a rare smooth transition to the grass of south-west London.
The 31-year-old Spaniard, beset by chronic knee problems, has struggled to adapt to the low bounce on grass in the latter stages of his career.
He hasn’t been past the fourth round at Wimbledon since 2011, losing to players ranked outside the top 100 on each of his last four visits.
But after missing Wimbledon due to a wrist injury last season and opting against playing a grass-court event after Roland Garros, Nadal had the ideal opponent to get up and running.
Millman, ranked 137th, was playing only his second Tour-level match this year after missing five months with a hip injury.
He was no match for a rampant Nadal and the 15-time Grand Slam champion blitzed his way to victory with a barrage of his trademark top-spin forehands.