Brady, who lost to Naomi Osaka in her first major final last month in Melbourne, made 25 unforced errors against her Estonian opponent in a 6-1 6-2 loss.

Kontaveit had only nine unforced errors and didn't face a single break point against the seventh-seeded American.

"I was expecting a very, very tough match but I'm very happy with the way I played and very pleased to get to the second round," Kontaveit said.

Kontaveit will play three-time grand slam champion Angelique Kerber in the second round after the German beat wildcard Cagla Buyukakcay of Turkey 6-4 6-2.

Garbine Muguruza beat Veronika Kudermetova 6-2 7-6 (7-4) to book a second-round match with third seed and last year's Doha winner, Aryna Sabalenka, who had a first-round bye.

"Good match ahead," Muguruza said.

"I'm excited to face these top players. I feel like every match is hard."

Eighth-seeded Victoria Azarenka needed six match points to get past veteran Svetlana Kuznetsova 6-2 6-3.

Azarenka will play Elena Rybakina or Laura Siegemund in the second round.

Kiki Bertens returned after five months off the tour and was dumped 6-0 6-2 by Jelena Ostapenko.

It was the 11th-ranked Dutch player's first match since a fourth-round loss at the French Open in October and a subsequent achilles tendon operation.

She missed the Australian Open to build up fitness.

Maria Sakkari eased past Mayar Sherif 6-06-3 in the first round.

Australian Associated Press