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Adopted Aussie Ajla Tomljanovic is through to the second round in Indian Wells following an impressive win over Alize Cornet.

Ajla Tomljanovic has continued her hot start to the 2019 with an impressive first-round win at the prestigious WTA event in Indian Wells.

While fellow Australians Samantha Stosur and Priscilla Hon bowed out, Tomljanovic dispatched Frenchwoman Alize Cornet 7-5 6-3 on Friday.

The Croatian-born 25-year-old climbed to a career-high No.40 in the world last month following runs to the final in Thailand and quarters in Qatar.

Tomljanovic next faces ninth-seeded Belarusian Aryna Sabalenka.

Stosur departed the Californian desert after a 6-2 6-3 loss to American wildcard Madison Brengle, while Hon's charge from qualifying came to an abrupt end with a 6-1 6-1 drubbing at the hands of Russian Natalia Vikhlyantseva.

Jordan Thompson was the only Australian to progress in the men's draw, with John Millman and Matt Ebden both crashing out in straight sets.

Thompson earned a shot at Austrian seventh seed Dominic Thiem with a thrilling 6-4 6-7 (8-10) 7-6 (7-5) win over Argentine Federico Delbonis.

But Millman succumbed 6-1 6-3 to German Jan-Lennard-Struff after veteran tiebreak specialist Ivo Karlovic eliminated Ebden 7-6 (7-3) 7-6 (7-3).

After enjoying first-round byes, Aussie seeds Ashleigh Barty, Alex de Minaur and Nick Kyrgios all open their campaigns on the weekend.

Barty takes on German Tatjana Maria on Saturday, with de Minaur playing American qualifier Marcos Giron on Sunday when Kyrgios, fresh off his title success in Acapulco last week, opens against German Philipp Kohlschreiber.