Serena Williams would meet a fellow American seed, either number 15 Sloane Stephens or number 23 Jamie Hampton, in the fourth round. Stephens defeated Williams in the Australian Open quarter-finals back in January.
Williams, seeking her 17th Grand Slam title and fifth US Open crown, beat 77th-ranked Galina Voskoboeva 6-3, 6-0. Williams won the last eight games, breaking to capture each set, and advanced in 69 minutes.
"She's back and fiery!" the announcer told the crowd, as Williams warmed up for the first-round match, which marked her 58th trip to a Grand Slam tournament.
Sania Mirza and her partner Anastasia Rodionova crashed out of the Estoril Open after losing to the Kazakh pair of Yaroslava Shvedova and Galina Voskobo 6-3 7-6 (6) in the women's doubles semi-finals.
Reigning French Open champ Li Na of China rallied to win her opening second-round match at Indian Wells on Friday, beating Galina Voskoboeva 3-6, 6-3, 6-3.
Spaniard Maria Jose Martinez Sanchez beat Kazakhstan's Galina Voskoboeva in the final of the $220,000 Hansol Korea Open on Sunday to win her fifth WTA title.