The 15-time Grand Slam champion, who lost in the third round of the Indian Wells Masters last week, overcame the Australian 7-6, 6-2 to reach the third round of the Association of Tennis Professionals Masters 1000 tournament at Hard Rock Stadium.

Djokovic will take on Federico Delbonis next after the Argentinian beat 32nd seed John Millman of Australia 7-5, 3-6, 7-6.

"I've had quite a lot of court time between my Indian Wells loss in singles and tonight's match," the Serbian said.

"I've worked on everything I need to work on. 

"Now it's just a matter of time to build the momentum and build that match play."

Dominic Thiem of Austria, who beat Roger Federer to win the Indian Wells Masters, crashed out at the second-round stage as he suffered a shock 6-4, 6-4 loss to Poland's Hubert Hurkacz.

Fifth seed Kei Nishikori is also out after he was beaten 2-6, 6-2, 6-3 by Dušan Lajović of Serbia.

In the women's draw, top seed Naomi Osaka of Japan needed three sets to edge past Yanina Wickmayer of Belgium at the Women's Tennis Association Premier Mandatory event.

Osaka looked on course for a comfortable win but dropped the second set before sealing a 6-0, 6-7, 6-1 victory.

Romania's Simona Halep is also through after the second seed ousted American Taylor Townsend 6-1, 6-3.

Twenty-three time Grand Slam champion Serena Williams was made to work hard for her place in the third round, the American recording a 6-3, 1-6, 6-1 win over Sweden's Rebecca Peterson.

The men's and women's tournaments continue tomorrow.