The 11th-seeded Clijsters seemed to twist her left ankle midway through the first set after taking a tumble, and then fought off four match points to overcome the fifth-seeded Na, 4-6, 7-6 (8-6), 6-4 to reach the quarterfinals.
A four-time Grand Slam champ, Clijsters was behind 6-2 in the second set tiebreak, but somehow rallied by winning the next six points. She evened the tiebreak at 6-6 with a brilliant lob winner and then finished off the set when her Chinese opponent sent a return long.
Clijsters won the first four games of the third set, but Li rallied to close within 5-4, even fighting off a match point. The Belgian then ended the lengthy affair when Li sent a backhander into the net, one of 46 unforced errors by the 29-year-old.
Also Sunday, third-seeded Belarusian slugger Victoria Azarenka advanced to the quarterfinals. Azarenka, who titled in Sydney last week by beating Li Na in the marquee finale, beat veteran Czech left-hander Iveta Benesova, 6-2, 6-2. Azarenka has yet to drop a set at this year's first major.
The match, which lasted 77 minutes, saw Azarenka take advantage of 26 unforced errors from Benesova. Next up for Azarenka will be No. 8 seed Agnieszka Radwanska, who beat No. 22 seed Julia Goerges, 6-1, 6-1.
"It's going to be a really tough battle," Azarenka said. "Mentally it's difficult. She's a very difficult player to play against. But we'll see. I mean, I'm going to be out there trying my best and fight hard."
Azarenka, who is on a nine-match winning streak, moved to 4-0 all-time against Benesova.