Jessica Pegula continued her breakthrough run at the Australian Open by knocking out Elina Svitolina, while Ashleigh Barty eased through to the quarter-finals.
American Pegula, the world number 61, rallied after a nervous second set to wrap up an impressive 6-4 3-6 6-3 victory against fifth seed Svitolina.
Pegula, whose parents own the NFL's Buffalo Bills and NHL's Buffalo Sabres, had failed to go beyond the first round in all but two of her previous eight appearances at the slams but added Svitolina to a list of scalps that also includes two-time Australian Open champion Victoria Azarenka.
The 26-year-old said: "I can't get more confident – it is my best result yet. I was a little tentative in the beginning of the second, and was able to play a couple of good games at the end of the second to get the momentum into the third. I definitely felt like I was sliding off the rails a little bit."
For Svitolina, it was another slam where she has failed to take advantage of what appeared a golden chance to reach the final stages.
The Ukrainian said: "It was not a good day for me today. I was making way too many errors. I didn't feel very good today on the court. It's disappointing because I've been playing very good."
Vekic had heavy strapping applied to her right knee early in the second set and fared better thereafter but Brady held off the Croatian to reach her second slam quarter-final.
The 25-year-old, who was one of the 72 players forced to endure a hard quarantine, said of facing Pegula: "I'm super excited for her making her first grand slam quarter-final.
"I know the emotions that she's feeling. You feel like you're on cloud nine, definitely. She's playing great tennis. I think we both know each other so well and I'm really looking forward to it. It will be a lot of fun."
Barty has quickly settled back into the old routine after not playing since last February and made it eight victories in a row with a 6-3 6-4 success against American Shelby Rogers.
The world number one is yet to drop a set and always looked in control despite needing two chances to serve out the match.
Barty has made the quarter-finals then semi-finals the last two years and is the only top-20 player left in her half of the draw.
The Australian said: "We're not done yet. Obviously it's exciting to be in another quarter-final of a grand slam, particularly here in Australia.
"If we had looked at the way we were preparing during our pre-season, to have the start that we have had so far is really encouraging, but certainly not satisfied with where we're at at the moment."
In the last eight she will face Czech 25th seed Karolina Muchova, who staged another impressive comeback to beat Elise Mertens 7-6 (5) 7-5.
Muchova trailed 5-0 in the second set against Karolina Pliskova in the last round before winning seven games in a row and was 4-0 down in the opening set here.
Williams has been chasing a record-equalling 24th grand slam singles title since returning from maternity leave nearly three years ago and her coach, Patrick Mouratoglou, is optimistic this can be the one where she gets across the line.
He said: "I don't think she needs that validation. But clearly she came back to tennis to win some other grand slams, so that's for sure the goal.
"Is she moving better than the last three years? Yes, for sure. If you can't move well, there is no Plan B. The only plan is attack. I think it cost her a few important matches.
"So we have decided to find a way to bring back the footwork that she used to have in the past. I feel like she's done a great job."