Ajla Tomljanovic has bowed out of the Gippsland Trophy Australian Open warm-up tournament in Melbourne after a hard-fought battle with veteran Alize Cornet.

Australia’s No.2 behind Ash Barty, Tomljanovic got off to a flying start before the French woman clawed her way back to eke out a 5-7 6-1 6-3 victory in a grinding contest on Margaret Court Arena.

Heading into the third set Cornet, ranked world No. 53, got an early break and Tomljanovic missed her opportunity to level before fading away.

Tomljanovic, 27, has had a lean run at Melbourne Park, never moving past the second round of the Australian Open.

But the world No. 69 has shown her commitment by heading to Abu Dhabi for a tournament last month where she was eliminated by world No. 7 Aryna Sabalenka in a tight contest.

Daria Gavrilova was the only Australian to advance to the second round of the WTA event in Melbourne so far, with world No.1 Barty in action on Tuesday after a first-round bye.