Henin closed out the victory by winning a second-set tiebreaker. She was ranked 294th, Clijsters 513th.
With the series now at 12-all, the Belgians will play another tiebreaker Monday on a slightly grander stage: Wimbledon. They'll meet in the fourth round.
"It's a great opportunity for both of us," Henin said. "To play each other again in a Grand Slam, I think it's something we couldn't expect a year ago. It's going to be interesting, very exciting."
A year ago, the two Grand Slam champions were retired, but career comebacks brought them back to Wimbledon — a tournament neither has won. Clijsters last played at the All England Club in 2006, Henin in 2007.
They've played each other twice this year, with Clijsters winning both times, but there are no hard feelings. The edge the rivalry had in its early years has softened for the two former No. 1s.
"It's obviously not the same as in the beginning," Clijsters said. "We've definitely grown up. We've had great times together playing Fed Cup and just messaging each other on phones, teasing each other — fun, you know. That's how I would have liked it to have always been."
Henin said she and Clijsters bonded in recent years playing Fed Cup together for Belgium.
"We're adults now, and we have a lot of respect," Henin said. "On the court we both want to win, but the relationship is very good."
Six-time champion Federer, pushed to nine sets in the first two rounds, had his easiest match of the week and beat Arnaud Clement 6-2, 6-4, 6-2. Melzer, seeded 16th after reaching the semifinals at the French Open this month, advanced to the fourth round at Wimbledon for the first time by beating Feliciano Lopez 4-6, 6-3, 6-2, 6-4.
Melzer is 29, Federer 28. They were junior doubles partners at the world championships in 1998.
"We go way back," Federer said. "Funny thing is, I've never played him."
No. 5-seeded Andy Roddick held every service game and beat Philipp Kohlschreiber 7-5, 6-7 (5), 6-3, 6-3. Roddick's opponent Monday will be Yen-hsun Lu, the first Taiwanese man to make the fourth round of a Grand Slam. He advanced when Florian Mayer retired with an injury trailing 6-4, 6-4, 2-1.
No. 3 Novak Djokovic will play 2002 champion Lleyton Hewitt in the fourth round. Djokovic advanced by beating No. 28 Albert Montanes 6-1, 6-4, 6-4, and the No. 15-seeded Hewitt defeated No. 21 Gael Monfils 6-3, 7-6 (9), 6-4.
Among those eliminated Friday was marathon man John Isner, playing for the fourth day in a row. After winning the longest match in tennis history, he lost quickly to unseeded Thiemo de Bakker, 6-0, 6-3, 6-2.
"Really just anything but tennis," he said. "I'll watch sports. I'll take in the World Cup. I'll go fishing. I'll do whatever. Just anything away from the tennis court."