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No.5 seed Elina Svitolina made it three straight-sets wins in as many matches through the first week of the Australian Open courtesy of a 6-4, 6-0 win over No.26 seed Yulia Putintseva on Saturday.

After losing the pair's first meeting back in 2012, Svitolina has now won six straight matches against her former junior peer, including four in straight sets. 

"I was expecting a tough battle today. We played some epic matches in the past. For me, was just important to play aggressive," Svitolina told reporters after the win.

"She has a very different game style from what I played my last two rounds, so it wasn't easy at the beginning to adjust. As soon as I was feeling better, I just stepped my game, and it was quite a comfortable win after."

A break down twice in the first set, Svitolina found her form in the set's late stages to sprint through to a 83-minute victory: from 4-3, down the Ukrainian won nine straight games to book a spot in the second week of the Australian Open for a third time. 

"It was very tough at the beginning. I did few errors that I hoped I would not do. She was playing good at the beginning. She was making lots of balls back. She was really playing good. For me, the key was just to try to find my game, try to deal with what she's giving. I think I dealt with that quite good. I was very happy I could win from 3-4 to, nine games in a row."

- Elina Svitolina on her third-round victory

The two-time quarterfinalist will next face breakout American Jessica Pegula, who rolled past Kristina Mladenovic, 6-2, 6-1, to seal a spot in her first fourth round of a Grand Slam for the first time.

The pair played in Abu Dhabi last month in the first tournament of the season, where Svitolina earned a 6-4, 6-3 victory in the first round.

"She's playing very aggressive," Svitolina said of the American. "I think she picked up her game quite good for the past I think year. I'm expecting a tough battle against her. She's a good competitor. It's going to be a tough one."

Saturday's victory was Pegula's second over Mladenovic in as many weeks, as she also beat the Frenchwoman in the first round of the Yarra Valley Classic.

"It's the first time I've been in the fourth round. It's a new experience for me. It's a new experience being second week of singles. I've done it in doubles. Maybe that helps a little bit. Definitely it's all new to me. I'm just trying to enjoy it... It's definitely still new, but that's what makes it fun. It's exciting."

- Jessica Pegula

Needing just 68 minutes to sail through the match inside John Cain Arena, Pegula hammered 21 winners and broke serve six times.

"I think I'm just playing with a lot of confidence and being really aggressive. I'm attacking a lot with my forehand and keeping people pressured at all times," Pegula told Tennis Channel after the match.

"I'm playing my return games really well, my serve games smart and I think that things are just clicking right now. This year, [my mindset] switched to just winning a round at a Slam to, 'Why can't I go deep at a Slam?' With setting my goals a little bit higher, plus the confidence from last year, I think it just happens. I'm just glad it's coming together right now."

On Svitolina, the American added: "We played in Abu Dhabi and it was close. Even though I lost in straights, I know with her, when I get my chances, I have to take them and do the best I can. I'm just going out there, playing my game and adapting when I need to. I'm just going to stick to my game plan and try to take my chances."

Brady, Vekic set round of 16 match

In the other round of 16 in this section of the draw, No.22 seed Jennifer Brady and No.26 seed Donna Vekic will square off for the right to play in their first Australian Open quarterfinal.

The two seeds had contrasting passage through to the fourth round with Brady easing to a 6-1, 6-3 victory over Slovenian qualifier Kaja Juvan, and Vekic saving a match point to overcome Kaia Kanepi, 5-7, 7-6(2), 6-4 in over two-and-a-half hours.

A largely routine victory for the American 25-year-old was highlighted by an 18-minute hold of serve in the penultimate game of the match: a nine-deuce game in all where she saved six break points.

"I think sometimes the score doesn't really reflect the toughness of the match," Brady said. "I think I was feeling pretty good in the first set. Then towards the end of the second set, I mean, I was getting a little bit nervous. She started playing a little bit more aggressive, started making me play a little bit more.

"I think sometimes you're not only battling someone on the other side of the court but also yourself. I mean, some people may find that a hurdle, making the second week of a Grand Slam. Definitely, I think everybody wants to make the fourth round and better.

"I was also thinking about that a little bit today in my match. Okay, maybe I have a little bit more experience than my opponent. Regardless of how I'm feeling, maybe she's feeling a little bit nervous as well."

From 7-5, 3-0 down, Vekic played her best with her back against the wall: after failing to convert any one of five break points at 4-4 in the second set, the Croatian denied the Estonian victory in her ensuing service game.

A forehand winner erased Kanepi's lone opportunity to win the match, and Vekic slowly wrestled control of the match from there. After seeing a 3-1 lead slip away in the decider, the No.26 seed held serve from 0-30 down at 4-4 before securing the victory with a final break of serve.

Vekic has now reached the fourth round at all four Grand Slams, with Saturday's dramatic victory earning her the milestone in her ninth Australian Open appearance.

"I was actually pretty pissed that I was a match point down because the game before I had a couple of break points on her serve, and I thought I was playing better. I thought the momentum was switching a little bit towards my side, so I was like, 'Okay, how am I a match point down, I don't want it to be over.' I just really went for my shots, and in the tiebreak I felt like, 'Okay, this set is mine.'"

- Donna Vekic

Both Brady and Vekic are chasing their second career Grand Slam quarterfinal, and the Croatian holds a 1-0 head-to-head edge. Their lone previous meeting came three years ago on clay in Rome, where Vekic won, 3-6, 6-3, 6-1.

"'m really happy. I've never played the second week in Australia, so I think this is my worst Slam when it comes to results," Vekic said.

"It might sound a bit weird because I'm in the second week, but I think I'm still far from my best tennis, so hopefully I can keep improving. I'm happy that I have a chance to play another match."