Naomi Osaka took another confident step in her comeback from maternity leave by easing past Elisabetta Cocciaretto 6-3 6-4 on Wednesday to move into the second round of the Miami Open, where another returning mother awaits.

Cocciaretto, ranked 51st in the world, represented a potentially tricky first test for Osaka with the Italian coming into Miami having won the WTA 125 event in Charleston last week.

But the step up in class proved too much as Osaka showed flashes of the form that carried her to four Grand Slam crowns, breaking Cocciaretto at the first opportunity while never allowing her opponent a break chance in the opening set.

Osaka needed just one break in the second, too, to get the job done, closing out the contest with an ace on her second match point.

The Japanese player next faces Ukrainian 15th seed Elina Svitolina, who is less than year into her return from maternity leave.

"I was watching her last year and I was admiring all her runs in Wimbledon," said Osaka of Svitolina's run to the semi-finals at Wimbledon. "It's going to be a really incredible honour to play against her."

Earlier on Hard Rock Stadium court, Sloane Stephens celebrated her 31st birthday by beating Germany's Angelique Kerber 6-2 6-3 in a one-sided battle between former Grand Slam champions.

Florida native and 2018 Miami champion Stephens converted four of her eight break point chances against Kerber and dropped serve once in the 70-minute match.

"I came out with a gameplan, I was very clear with that, and I didn't really deviate from that," Stephens said during her on-court interview.

"I just tried to play the best I could and give the best effort I could and I'm happy to be through with the win."

Up next for the 2017 US Open champion, who fell in the third round at Indian Wells last week, is Romania's Sorana Cirstea.

World number 41 Stephens was barely tested in the first set which she wrapped up with her second break, this one coming to love.

Kerber, a three-time Grand Slam winner who returned to the tour in January after an 18-month maternity break, was looking to build on her fourth-round showing at Indian Wells.

She appeared more comfortable early in the second set but was ultimately undone by a rash of errors.

Stephens took advantage and consolidated a break for a 5-2 lead and then went on to serve out the match with a routine hold that she punctuated with a forehand to the open court.

In an all-American first round match-up, qualifier Katie Volynets upset compatriot and former Australian Open champion Sofia Kenin 6-2 4-6 6-3, while Croatia's Donna Vekic was a 6-4 2-6 6-2 winner against big-hitting Czech Karolina Pliskova.