The American dominated with her first serve and grabbed more than half of the return points to put Eugenie under all kind of pressure and break her six times from 13 opportunities.
"So I knew "Serena, you've got to come out hot, you've got to come out firing, she's a really good player and I haven't had many matches since last year".
Williams responded with a lift in intensity, going on a five-game winning streak to settle the match.
Williams responded in dominant fashion, and did not drop another game on her way to ending the match with a drive-volley victor.
"So she's ready. She's ready to compete and when Serena's ready to compete, she's ready to win".
Williams is in Australia aiming for a 24th Grand Slam singles title.
Brexit deal defeat sparks fresh hard border fear
Moments after the defeat Labour Party leader Jeremy Corbyn announced that he had tabled a vote of no confidence in the Government. When Foster said "we never had a hard border" in Ireland, however, people responded in disbelief.
Ranked No. 59, Yastremska is also the highest seed Williams has yet to face in this tournament, so the fact that Williams is speeding through matches is less headline material than a reminder that she is playing the tennis we expect her to play and this tournament is hers to lose. I was screaming the same time she was screaming.
"I would probably say with the career she's had, that she's not even finished at this point, then yes, I would say so", she said.
"It wasn't an easy match tonight - Genie has been to the finals at Wimbledon", Williams said.
Monfils was spotted in Svitolina's player box during her 6-4 6-1 victory over Viktoria Kuzmova in the second round, leading to an awkward moment when she was asked about it during her on-court interview. Williams is 8-2 in her career against Halep and has faced her only twice in Slams, taking both meetings.
"When I go on court tomorrow I won't think about everything". "Nike always wants to make and incredibly strong, powerful statement for moms that are trying to get back to get fit, so that was basically it for me". I'm going to try to show my best tennis. "That's what she does well", Bouchard said.
"I think it might happen", Mouratoglou said of Williams' hopes for a 24th Grand Slam title. "You're so nice, so sweet, "' Yastremska recounted.