Reigning Miami Open champion Ashleigh Barty fended off a match point to win in three sets against Kristina Kucova.
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.
Ash Barty will begin her WTA Adelaide International title defence against Danielle Rose Collins, who overcame Zheng Saisai.
It is opening up nicely at Roland Garros for Elina Svitolina after Simona Halep and Kiki Bertens became the latest seeds to fall in Paris.
A dominant victory boosted the confidence of Simona Halep, while Elise Mertens' tournament was ended by Caroline Garcia.
Number one seed Svetlana Kuznetsova awaits qualifier Eugenie Bouchard in the second round in Istanbul.
Naomi Osaka was pushed before getting past Marta Kostyuk in the US Open third round.
Runner-up in 2016, Karolina Pliskova made a second-round exit at the US Open.
After a couple of tough weeks, Sofia Kenin came through her opener in Lyon against Vitalia Diatchenko.