Seven-time champion Serena Williams comforted opponent Dayana Yastremska after powering past the teenager into the Australian Open fourth round.

Williams beat the 18-year-old Ukrainian 6-2 6-1 in one hour and seven minutes and did not drop a service game.

“You’re gonna make it, don’t cry”, Williams, 37, told a tearful Yastremska following her victory. The American will face Romanian world number one Simona Halep next after she beat Serena’s older sister Venus.

“I thought she did really amazing,” Williams said when asked about the future of Yastremska, who was not even born when the American won the first of her 23 Grand Slam singles titles in 1999.

“She came out swinging and to be so young, she came out ready to go. When I was young I played against so many people and everyone I faced was intimidating and not easy. You just go out and swing and do the best you can.”

Williams is favourite to win a record-equalling 24th Grand Slam singles title in Melbourne and her performance in the third round showed why.

She put youngster Yastremska under immediate pressure, breaking in the first game and winning four games in a row. The occasion seemed to have got the better of the Ukrainian – a promising talent who could only provide brief glimpses of her ability and could not hide inconsistencies with her serve.

But Williams was ruthless and looks firmly on course to win a record-extending eighth Australian Open title.

With defending champion Caroline Wozniacki exiting on Friday and rivals Naomi Osaka – the fourth seed – and Elina Svitolina – the sixth seed – being forced to fight back to scrape their way into the fourth round, it is so far falling into place for Williams.

Her toughest test yet will be in the next round where a mouth-watering tie with Halep awaits.