Sloane Stephens had lost in the first round in Monterrey and Melbourne earlier this year but won in Miami on Wednesday.
Madison Keys had not played on tour since September, but the American looked in good shape as she began her season in Doha.
Karolina Pliskova took out her frustrations during a third-round defeat, but Ash Barty was able to reach week two in Melbourne.
Kristina Mladenovic lost after an umpire's controversial call turned the momentum of her French Open clash with Laura Siegemund.
Seemingly cruising into the third round, Kristina Mladenovic lost 12 of the next 13 games and then ranted at the US Open conditions.
Runner-up in 2016, Karolina Pliskova made a second-round exit at the US Open.
Kristina Mladenovic says she has to abide by stricter protocols at Flushing Meadows after practicing and playing cards with Benoit Paire.
Jacqueline Cristian had former doubles partner Sofia Kenin on the ropes, but the Australian Open champion emerged triumphant in Lyon.
Chloe Paquet dominated Kristina Mladenovic in the first set, but the second seed rallied to reach the second round in Lyon.
Ons Jabeur pushed Simona Halep all the way, but the two-time grand slam champion was not to be denied a place in the last eight in Dubai.