The Ukrainian sixth seed, 24, came through a closely contested opening set to win 6-4 6-1 on Rod Laver Arena.

Following her victory, Svitolina was asked on court about French male player Monfils, who was spotted in her box.

"We are here for tennis, so that's why it was a bit strange," she said later.

"I didn't really expect to be asked that because I just finished my match.

"He's there for me, he's supporting me, and I'm there for him as well. He understands, I understand, what we're going through. It's great."

Svitolina will face China's Zhang Shuai next.

Czech seventh seed Karolina Pliskova recovered from losing the opening set to beat American Madison Brengle 4-6 6-1 6-0 on Melbourne Arena.

US Open champion Naomi Osaka was also made to work harder than she may have wanted, coming from a break down in the second set to win 6-2 6-4 against Slovenia's Tamara Zidansek.

American Madison Keys, who reached the semi-finals four years ago, set up a third-round meeting with Belgium's Elise Mertens after easing past Russian Anastasia Potapova 6-3 6-4.

Mertens, a semi-finalist in Melbourne herself last year, had earlier beaten Russia's Margarita Gasparyan 6-1 7-5.

Latvian 13th seed Anastasija Sevastova was taken to three sets by Canadian qualifier Bianca Andreescu, eventually winning 6-3 3-6 6-2.

Meanwhile, China's Wang Qiang and Italy's Camila Giorgi took less than an hour to book their third-round spots, beating Serbian Aleksandra Krunic 6-2 6-3 and Polish qualifier Iga Swiatek 6-2 6-0, respectively.