The US Open last 16 looms for world number one Serena Williams, plus Agnieszka Radwanska and Simona Halep.
Williams made Open Era history as she eased past Johanna Larsson at Flushing Meadows on Saturday.
Polish fourth seed Radwanska accounted for Caroline Garcia in straight sets, while fifth-seeded Romanian Halep survived to beat Timea Babos in New York.
Karolina Pliskova and birthday girl Carla Suarez Navarro were also third-round winners.
WIN NUMBER 307 AND COUNTING
Williams became the most winningest women in the Open Era after defeating Larsson 6-2 6-1.
Yet to drop a set at the year's final major, Williams racked up four breaks of serve to move level with Roger Federer on 307 grand slam wins - taking her past Martina Navratilova in the process.
The 22-time grand-slam champion wasted no time on Saturday, claiming the opening set in just 37 minutes as she produced 13 winners.
If the first set was routine, the second was a procession as Williams upped the tempo, not giving Larsson a chance to settle as she rattled off five games in a row to progress to a fourth-round clash with Yaroslava Shvedova, who prevailed 6-2 7-5 against Shuai Zhang.
HALEP AVOIDS UPSET IN COMEBACK
The US Open hopeful outlasted 31st seed Babos 6-1 2-6 6-4 in a dramatic match.
Halep appeared poised to ease through to the round of 16 after taking the first set in just 24 minutes but Babos found her composure, claiming the second to force a decider.
Babos was then in the box seat, earning a 3-1 lead before Halep rallied for a 4-3 turnaround and an eventual spot in the next round.
Next up for Halep is 11th-seeded Spaniard Navarro, who was too good for fellow seed Elena Vesnina 6-4 6-3.
RADWANSKA IN THE HUNT
One of three players in the mix for the world number one ranking, Radwanska dispatched Garcia 6-2 6-3.
Radwanska, who can go top of the WTA standings if she makes the final and Angelique Kerber fails to reach the fourth round, benefitted from Garcia's error-riddled performance as the Frenchwoman tallied 34 unforced errors in 70 minutes.
The Pole will meet Ana Konjuh in the fourth around after the latter overcame Varvara Lepchenko 6-3 3-6 6-2.
Venus Williams - the sixth seed - starred under the lights at Arthur Ashe Stadium, blitzing Laura Siegemund 6-1 6-2.
Next up is 10th seed Pliskova, who upstaged Anastasia Pavlyuchenkova 6-2 6-4.
BREAKTHROUGH FOR PLISKOVA AND KONJUH
Pliskova's straight-sets win ensured she reached the fourth round of a grand slam for the first time in her career.
Croatian teenager Konjuh, 18, also achieved the feat.
Babos' loss meant the Bulgarian holds a 0-7 career record against top-five players, while she is 0-3 when facing Halep.
KERBER KICKS OFF LAST 16
The Olympic Games silver medallist headlines Sunday's play, as she takes on two-time grand-slam champion Petra Kvitova. Roberta Vinci is up against Lesia Tsurenko, while Caroline Wozniacki faces Madison Keys.