The three-time defending champion won 6-0 2-0 after only 30 minutes at Arthur Ashe Stadium when Diatchenko retired with a left foot injury, advancing Williams into the second round at Flushing Meadows.
The 33-year-old American chases the first calendar Grand Slam since Steffi Graf in 1988 and a 22nd career major title to match Graf's Open Era record, two shy of Australian Margaret Court's all-time mark.
Top-ranked Novak Djokovic cruised into the men's second round but Japanese fourth seed Kei Nishikori crashed out after his runner-up effort last year.
"I felt the support and love on this journey and milestone I'm trying to take one match at a time," Williams said.
"I feel so good. I'm so ready. I'm at home, where it all began for me in '99. It all feels great."
Williams advanced to a second-round match against Dutch qualifier Kiki Bertens, who eliminated Croatian Mirjana Lucic-Baroni 3-6, 6-4, 6-2.
"If I can just stay relaxed and stay in the points and stay calm and stay happy out there, I have to look at it as I have nothing to lose."
That left 12th seed Belinda Bencic -- who ousted Bulgarian Sesil Karatancheva 6-1, 6-2 -- as the top-rated foe in Williams' half of the draw. Williams, who lost to Bencic in the Toronto semi-finals, could see the Swiss teen again in a quarter-final.
Williams, who owns six US and Australian Open and Wimbledon titles plus three French Open crowns, won her 22nd US Open match in a row since her last loss, to Aussie Samantha Stosur in the 2011 final. Williams has won eight Slam titles since then.