The 17-time Grand Slam champion had never lost to Seppi in 10 previous meetings, but made some uncharacteristic errors including nine double-faults — including one to surrender a mini break in the fourth-set tiebreaker.
Seppi, a 30-year-old Italian who had only advanced beyond the second round once at his nine previous trips to Melbourne Park, held his nerve despite some withering winners from Federer, who registered his 1,000th career match win when he collected the Brisbane International title earlier this month to open the season.
Federer has won the Australian title four times, and had reached the semifinals or better at Melbourne Park every year since winning the championship for the first time in 2004.
"I had to believe that I could win," said Seppi, who said he stuck out his racket and hoped for the best on match point — a forehand that sailed past Federer and landed in the corner. "I was just trying to stay relaxed and just focusing on every shot and to breathe calm and don't get nervous.
"I think I did pretty well. Very well. I'm very happy I could manage the emotions."
Eugenie Bouchard struggled through a scrappy opening set before getting on top in a 7-5, 6-0 third-round win over Carolina Garcia that featured 10 breaks of serve.
There were six service breaks by the time the scores were level at 4-4, but seventh-seeded Bouchard started finding rhythm late and got the crucial break in the 12th game.
"Yeah, I don't think it was the prettiest tennis out there," said Bouchard, who reached the semifinals in her first trip to Melbourne Park last year and went on to make the semifinals or better at two of the other three majors in a breakthrough season. "But I'm happy that I just kept going. Even if it wasn't going so well, I was able to turn it around."
Third-seeded Simona Halep advanced with a 6-4, 7-5 win over Bethanie Mattek-Sands, missing twice when she served for the match in the eighth and 10th games before finally serving out.
Halep, who opened the season by winning the Shenzhen Open in China, will next play Yanina Wickmayer, who beat No. 14-seeded Sara Errani 4-6, 6-4, 6-3.
"Here I started last year to play my best tennis. I (reached) my first quarterfinal in Grand Slams ... then I made final in French Open," Halep said. "I have more confidence now during Grand Slams and I believe I have my chance at every tournament."
No. 10 Ekaterina Makarova had a 6-4, 6-4 win over No. 22 Karolina Pliskova and No. 21 Peng Shuai beat Yaroslava Shvedova 7-6 (7), 6-3 to move into a possible fourth-round showdown with No. 2 Maria Sharapova, who was playing No. 31 Zarina Diyas in a night match.
Sixth-seeded Andy Murray beat Joao Sousa 6-1, 6-1, 7-5 to set up a 4th round clash with No. 10 Grigor Dimitrov.
Murray is attempting to become the first man to win the Australian Open after losing three times in the final. He lost to Novak Djokovic in 2013 and 2011 and Roger Federer in 2010.
Dimitrov had a tough third-rounder against 2006 Australian Open finalist Marcos Baghdatis before winning 4-6, 6-3, 3-6, 6-3, 6-3.
Seventh-seeded Tomas Berdych beat Viktor Troicki 6-4, 6-3, 6-4 , needing eight match points to clinch it.
"It looks not very nice on the paper — mostly, all of them on a big first serve," said Berdych, a semifinalist here last year and the 2010 Wimbledon runner-up. "It was a great save from him. I needed to wait one more game ... when the first chance came up, I served well and took it."