Then along came Roger Federer to flatten their hopes.
Federer has won four of his record 16 Grand Slam singles titles on Rod Laver Arena, and on Sunday night he more or less held a clinic — a 6-4, 6-2, 6-2 victory over Bernard Tomic to reach the quarter-finals for a 31st consecutive major.
He played the 19-year-old Aussie at his own game, but raised it a level: mixing soft, angled drop shots that just cleared the net with crisp groundstrokes that hit the lines and — for good measure — a leaping, backhand overhead.
"It was like boxing in the beginning. You don't want to take too many chances," Federer said, explaining why there weren't any service breaks until the ninth game, when he produced two drop shots for winners with Tomic stranded in the backcourt. "Had one game when I was starting to feel better, next thing you know I'm up a break. Maybe I broke his will there a bit."
Federer's quarter-final will be his 1,000th tour-level match. He plays 2009 U.S. Open champion Juan Martin del Potro, whom he once expected to rise to No. 1.
Clijsters, the defending champion, won despite limping on a badly sprained left ankle. She saved four match points in a tiebreaker en route to her 4-6, 7-6 (6), 6-4 win in a rematch of the 2011 final against Li Na. That put the four-time Grand Slam winner on course for a quarter-final against Caroline Wozniacki, who has held the year-end No. 1 ranking the last two seasons without winning a major.
Wozniacki is desperate to end her Grand Slam title drought, and improved her credentials marginally with a 6-0, 7-5 win over former No. 1 Jelena Jankovic in the last match Sunday night.
"My confidence is high, my fitness is good, my play is improving and I'm very positive," Wozniacki said. "If I play like I did today, Kim will have to really play well to beat me."
Clijsters has been a longtime favourite in Australia, dating to her time as Lleyton Hewitt's fiancee. The Belgian is married now to Brian Lynch and has a child, but is still known endearingly as "Aussie Kim" — a nickname she felt she truly earned only when she won the Australian title last year.
Clijsters came into the tournament with a hip injury. When she fell after spraining her ankle in the seventh game, there was concern her last Australian Open run might finish prematurely. She needed pain killers to get through the two-hour 23-minute match against Li. Now she's hoping ice treatment will help her recover in time for the quarter-finals.
"I knew if I could get through the 20 minutes, half hour (after the injury), I think the pain would go away a little bit and then maybe with the adrenaline I could just fly through it," she said. "I thought, 'I don't want to quit in my last time at the Australian Open.' I said in my mind, 'Keep fighting. You never know what happens on the other side of the court.'"
It turned out she was right.
Li, who won last year's French Open to become the first player from China to claim a Grand Slam singles title, was a set up and 6-2 in the tiebreaker. Her path to the quarter-finals seemed clear.
But her moments came and went. She had a chance to put Clijsters away with a big forehand but instead knocked a ball back across the net and was lobbed.
"Of course, I was nervous. If you're nervous, you could not think too much, right?" said Li, who broke down in tears in her post-match new conference. "Maybe 6-2 up in the tiebreak I was a little bit shocking."
Third-seeded Victoria Azarenka has flown under the radar so far, reaching the quarter-finals with a 6-2, 6-2 win over Iveta Benesova. She will next meet eighth-seeded Agnieszka Radwanska.
There's been plenty of attention on Serena Williams, who will be aiming for her 18th consecutive win at Melbourne Park when she plays Ekaterina Makarova of Russia on Monday. She won the 2009 and 2010 Australian titles but was sidelined at this stage 12 months ago with injuries.
Novak Djokovic won the men's title last year, starting a season in which he captured three of the four majors and finished with the top ranking. He's in action Monday night against Hewitt, the gnarled veteran who is trying to end a drought that dates to 1976 for local men at the Australian Open.
After Federer beat Tomic, the 30-year-old Hewitt is the only Australian left in the singles draws. That didn't make Federer any less popular in Australia, where he's aiming to equal Roy Emerson's record of five Australian titles.
Federer's last win over Del Potro at Melbourne Park was the Argentine's worst in a Grand Slam.
Del Potro figures to be more dangerous this time after beating Germany's Philipp Kohlschreiber 6-4, 6-2, 6-1 on Sunday.
He was sidelined for much of 2010 after wrist surgery, but improved his ranking from a low of No. 485 last January to his current position at No. 11.
"I missed him in that year when he got injured. I thought he had a chance for world No. 1 to be honest, he was playing that well. It's nice is to see him back."
If he can get past Del Potro, a possible semifinal against Rafael Nadal could await. They're in the same half of the draw for the first time since 2005.
Nadal had a convincing win over fellow Spaniard Feliciano Lopez on Sunday. The 2009 champion's right knee was heavily wrapped and his left ankle needed to be taped after three games of the first set. Afterward, he said he was fine.
He next plays Tomas Berdych, hoping to avoid a third consecutive quarter-final loss in Melbourne. He was injured in his last two quarter-finals, but says the knee should be OK this time.
"I had a bad experience last two years here," Nadal said. "It's tough have to go out of a tournament like Australia in quarter-finals."
Berdych beat Nicolas Almagro 4-6, 7-6 (5), 7-6 (3), 7-6 (2), then was jeered by the crowd at Hisense Arena after he refused to shake hands with his Spanish rival. The Czech was upset that Almagro had hit the ball straight at him while he was at the net during the fourth set.
"I think when you have a point and someone wants to hit you straight to your face, I don't see this as a nice moment," Berdych said during a post-match TV interview. "This is not the way how tennis is."