Wimbledon champion Simona Halep has overcome a tough first set as well as a wrist injury to advance to the Australian Open second round.

A finalist in 2018 at Melbourne Park, Halep saved three set points on Margaret Court Arena on Tuesday night before overcoming American Jennifer Brady 7-6 (7-5) 6-1.

Brady had good form coming into the tournament, taking down world No.1 Ashleigh Barty at the Brisbane International.

Romanian Halep, the fourth seed, had to have her wrist taped after taking a tumble mid-rally during the first set.

But the 28-year-old, who has reunited with her Australian coach Darren Cahill, said she hoped it wouldn’t hinder her in her second round match against either British qualifier Harriet Dart or Japan’s Misaki Doi.

“It’s quite painful,” Halep said after the match.

Halep found the going tough in the first set against the aggressive Brady, but got into a groove to dominate the second.

“I found my rhythm a bit more in the second and tried to move her move,” Halep said.

“I was stronger and my serve went better.”

Indeed Halep improved her first serve accuracy from 74 per cent to a very impressive 88 per cent in the second set as she overpowered the world No.49.

Halep, who also won the 2018 French Open title, said she was enjoying having Cahill back in her box after he split with the then world No. 1 later that year to spend more time with his family.

“It’s a very nice feeling to have him back in my team,” she said.