Williams, who lost in the fourth round of the Australian Open, the second round of the French Open and third round of Wimbledon, said she felt the pressure of getting to the quarters in New York.
"I finally made a quarterfinal this year!" Williams said in her on-court interview, raising her hands to the cheers of the crowd in Arthur Ashe Stadium. "I think I felt it in my service game. I'm like, 'Can I please make it to a Grand Slam quarters this year?'"
The top-seeded man, Novak Djokovic also rolled into the quarters on another hot, muggy day at Flushing Meadows, playing mostly mistake-free tennis in a 6-1, 7-5, 6-4 dismantling of 22-seeded Philipp Kohlschreiber of Germany.
For Djokovic, the 2011 U.S. Open champion, it marked his eighth straight quarterfinals at the tournament - 22nd consecutive Grand Slam tournament overall. The last time Djokovic was eliminated before the quarterfinals at a major was a third-round loss to Kohlschreiber at the 2009 French Open.
Asked to explain that consistency, Djokovic said, "I love the sport and I play it with a lot of passion." He then did a dance for the crowd at Louis Armstrong Stadium.
Next up for the Serb, who reached the U.S. Open final each of the past four years, will be a match against 2012 U.S. Open champion Andy Murray or ninth-seeded Jo-Wilfried Tsonga.
Williams next plays 11th-seeded Flavia Pennetta, a 7-5, 6-2 winner over 29th-seeded Casey Dellacqua.
Pennetta, who reached the semifinals of the U.S. Open last year, said she needed to do her best with the tools she has to have a chance against the No. 1-ranked Williams, who already holds 17 Grand Slam titles.
"You cannot invent something. I mean, you just have to play your tennis," Pennetta said. "Of course, she's better than me, but if I still believe I can beat her, maybe if she doesn't have a good day, I can do that."
Unlike the men's side, which entered Monday with only one major upset, No. 4 David Ferrer, the women's draw has been decimated. Only Williams, No. 7 Eugenie Bouchard and No. 10 Caroline Wozniacki have survived among the top 10 seeds going into the tournament's second week.
Victoria Azarenka, the No. 16 seed and U.S. Open finalist loser to Williams the last two years, sought a place in the quarterfinals with a night match against 145th-ranked qualifier Aleksandra Krunic. Bouchard was seeking her spot with a matchup against No. 17-seeded Ekatarina Makarova.
In other early action Monday, the No. 1 doubles team of Bob and Mike Bryan rolled on in their quest for a 100th career title with a 6-3, 7-6 (5) victory over U.S. countrymen Bradley Klahn and Tim Smyzek. The Bryans, who hold a record 15 Grand Slam tournament titles, have yet to drop a set on their road to the quarterfinals.
And the darling of the U.S. Open, 15-year-old CiCi Bellis, opened her pursuit of the junior girls' crown with a 6-1, 6-3 victory over Mexico's Renata Zarazua.
Bellis, the top-seeded junior, played in the grandstand, the third-largest venue, to accommodate fans eager to watch the 15-year-old prodigy. Bellis upset of 12th-seeded Dominika Cibulkova, the Australian Open runner-up, in the first round of the main draw.