World number one Simona Halep avoided the dramas of her third round to ease into the quarter-finals of the Australian Open with a 6-3 6-2 victory over Naomi Osaka.

The 26-year-old looked to be heading home when Lauren Davis held three match points in their titanic encounter on Saturday but recovered to win 15-13 in the deciding set.

With Halep already troubled by the ankle injury she suffered in her first-round win, Japanese-American Osaka, one of the brightest young talents – and biggest hitters – in the game, looked a potentially tricky obstacle.

The 20-year-old began well and had an early break but Halep quickly began to break down Osaka’s game with her variety, athleticism and ability to turn defence into attack.

Halep needed just an hour and 19 minutes to wrap up victory and will play either sixth seed Karolina Pliskova or her fellow Czech Barbora Strycova in the last eight.

The top seed, who has made no secret that her focus is solely trained on winning a first grand slam title, said: “It was a great match. I’m really happy that I’m in the quarter-finals. I didn’t expect that when I started the tournament because of the injury but today I played well.

“This tournament looks like a marathon for me. The injury is still there but I try not to think too much about it and give everything because after this hopefully I’ll have a few days off.”