Williams, launching her latest bid to rewrite the record books, started strong and didn't let up in 6-3, 6-3 victory over 29th-ranked Ekaterina Makarova.
The US world number one appeared untroubled by the balky right shoulder that has hindered her in recent weeks, delivering a dozen aces and 27 winners overall in the 63-minute contest.
"I knew today I needed to be focused because I've played her. She's gotten to the semi-finals. She goes deep in majors," Williams said of the Russian left-hander who beat her in the fourth round of the 2012 Australian Open.
"She knows how to play big matches on big courts. She's not intimidated. I knew I had to really come out today. It was my only option really."
Williams said she wouldn't know until she'd slept on it how her shoulder might respond to the effort.
"Every day, I'll just see how it goes," said Williams, who is chasing a record seventh title on the hardcourts of Flushing Meadows where she first triumphed in 1999.
A victory would see her break the Open Era record of 22 Grand Slam titles she now shares with German Steffi Graf and close in on Margaret Court's all-time mark of 24 major titles.
While Williams has struggled since Wimbledon, Murray went from claiming a second title at the All England club to a successful defence of his Olympic gold in Rio.
Vying to become the fourth man in the Open Era to reach all four major finals in a calendar year, Murray, too, produced a dominant service performance in a 6-3, 6-2, 6-2 victory over Czech Lukas Rosol.
"I don't think I had any break points against me, which is very good," the Scot said.
Before the floodlights came up, Serena's elder sister Venus claimed a Grand Slam record of her own as her 6-2, 5-7, 6-4 victory over Ukraine's Kateryna Kozlova marked her 72nd appearance in the main draw of a major.
The 36-year-old Venus, enjoying a resurgence in a 2016 season that includes a WTA title in Taiwan, survived 63 unforced errors against the rising 22-year-old, although she was pleased that her aggressive approach also yielded 46 winners.
"The good part is I'm playing the game I want to play, I'm playing aggressively and moving forward," Venus said.
"It's just about making a few less errors and it's a completely different story."
Fourth seed Agnieszka Radwanska of Poland, trying to make it to the quarter-finals in New York for the first time, breezed past US qualifier Jessica Pegula 6-1, 6-1 and fifth-seeded Romanian Simona Halep also eased through with a 6-0, 6-2 victory over Belgian Kirsten Flipkens.
Men's third seed Stan Wawrinka of Switzerland, a two-time semi-finalist, reached the second round with a 7-6 (7/4), 6-4, 6-4 win over Spain's Fernando Verdasco.
Kei Nishikori, who became Asia's first men's Grand Slam finalist in New York in 2014, when he fell to Marin Cilic in the final, also advanced, downing German Benjamin Becker 6-1, 6-1, 3-6, 6-3. Eighth-seeded Dominic Thiem of Austria needed five sets to secure his second-round spot, downing Australia's John Millman 6-3, 2-6, 5-7, 6-4, 6-3.
Juan Martin del Potro, the 2009 US Open champion whose career was nearly ended by three wrist surgeries, advanced with a 6-4, 6-4, 7-6 (7/3) victory over fellow Argentine Diego Schwartzman.
There was a little record-setting on the men's side as well, with Croatian Ivo Karlovic belting a US Open record of 61 aces in a 4-6, 7-6 (7/4), 6-7 (4/7), 7-6 (7/5), 7-5 win over Taiwan's Lu Yen-Hsun.
Karlovic, 37, beat the previous best of 49 aces for one match in New York established by Richard Krajicek in 1999.
"I knew there were a lot of aces because there was a period when almost every serve was an ace," Karlovic said.