Men's third seed Novak Djokovic, women's number one Caroline Wozniacki and Russian Maria Sharapova also reached the last 16 on a hot day at Melbourne Park.
Federer, recovered from his five-set thriller against Gilles Simon, handed out a 6-3, 6-3, 6-1 beating to ponytailed Belgian Xavier Malisse, whom he has known since his junior days.
In the process he broke Stefan Edberg's record for the most Australian Open victories in the Open Era and took an important step towards a fifth title - and the chance to deny Rafael Nadal a sweep of the Grand Slam crowns.
"It's very nice to take the record but Edberg still stays my idol," Federer told the crowd on Rod Laver Arena.
As temperatures rose past 32 deg C (90 F) on the tournament's hottest day, 2004 winner Henin was floored by Russia's Svetlana Kuznetsova, who held her nerve in a gripping tiebreak to win 6-4, 7-6 (10/8).
The seven-time Grand Slam champion, 28, has been struggling with an elbow injury after ending a brief retirement last year, and has not performed so badly at a major since Wimbledon 2006.
"I decided to play not being 100 percent. It's been difficult in the last three days on my elbow and I just did everything that I could to make it okay, but it wasn't enough," Henin said.
Earlier Djokovic's quest to upset Nadal and Federer's Grand Slam stranglehold received a helping hand when fellow Serb Viktor Troicki retired hurt after going a set down.
After Juan Martin del Potro's demise late Thursday, third seed Djokovic is the only player left in Melbourne, other than Nadal and Federer, to have won a Grand Slam since 2006. He said he was not sorry to play a short match.
"I think I had enough tennis already in the last couple of weeks. It's good that you don't spend that much time on the court, maybe save some energy," Djokovic said. "But I'm going to be ready for the next match."
Meanwhile, Wozniacki took sweet revenge on Slovakian pocket rocket Dominika Cibulkova, whose shock victory at last week's Sydney International raised new questions about the Dane's credibility as world number one.
Wozniacki was broken three times but cashed in on an even higher error-rate by Cibulkova, the top 100's shortest player at five foot three inches (1.61 metres), wrapping it up 6-4, 6-3 in 1hr 32min.
Afterwards, the 20-year-old Dane turned on journalists who accused her of giving boring press conferences.
"Yesterday (I was told) my press conferences were kind of boring, that I always gave the same answers," she said.
"I find it quite funny because I always get the same questions. I know what you're going to ask me already, so I'm just going to start with the answers."
Wozniacki then stunned media by rattling off a monologue answering the predictable questions she knew she would face.
French Open champion Francesca Schiavone eased past Monica Niculescu 6-0, 7-6 (7/2) and Latvian Anastasija Sevastova beat Vesna Manasieva 6-1, 6-3 to set up a last-16 meeting with Wozniacki.
Sharapova fought back from a set down before subduing Germany's Julia Goerges 4-6, 6-4, 6-4, while China's Li Na downed Barbora Zahlavova Strycova 6-2, 6-1 to revive memories of her run to last year's semi-finals.
Meanwhile Andy Roddick came from behind to see off Dutchman Robin Haase 2-6, 7-6 (7/2), 6-2, 6-2. In an eventful match, Haase rolled an ankle in the second game and hit shots with his back to the net and while leaping in mid-air.
Serbia's Troicki joined a growing injury list after Marcos Daniel retired from his match with Nadal, Karol Beck was forced out while playing Andy Murray and a dizzy David Nalbandian gave up on his encounter with Richard Berankis.