Rafael Nadal, meanwhile, has reached the fourth round, rebounding from his five-set, second-round win to beat No. 106-ranked Dudi Sela 6-1, 6-0, 7-5 in a third-round match lasting a little over two hours.
Federer made some uncharacteristic errors -- including nine double faults, one to surrender a mini-break in the last tiebreaker -- and fell 6-4, 7-6 (5), 4-6, 7-6 (5).
The 17-time Grand Slam champion was facing match point against Seppi for the first time in their 11 head-to-head meetings, and had control of the rally when he hit a deep forehand into the corner and followed it to the net.
The No. 46-ranked Seppi lunged to his right and stuck out his racket, more hopeful than confident, and guided the ball down the line. Federer let it go past, and glanced back to see it land inside the baseline.
"The way he hits it you think, 'This can't possibly land in.' You kind of go and you're there and you're like, 'No, I'm going to let it go,'" the second-seeded Federer said. "As you're telling yourself that, you look behind you and you already know it's done."
Federer had reached the semifinals or better at Melbourne Park ever since winning the first of his four Australian titles in 2004. He hadn't been ousted before the fourth round here since 2001. That changed in an instant.
"I don't know. Ask him how he felt hitting it," Federer said of the winning shot. "It's clearly a big blow because I actually hit my forehand pretty good."
Seppi was euphoric, but acknowledged that the defining shot of the match was not a calculated winner.
"Yeah, was for sure a strange shot," the 30-year-old Italian said. "At the beginning I thought I couldn't even reach the ball. Then, when I hit it, I didn't see it going there. I just saw when it bounced in.
"Was for sure one of the important shots of my life."
Seppi had only advanced beyond the second round once at his nine previous trips to the Australian Open. He held his nerve despite some withering winners from Federer, who registered his 1,000th career match win earlier this month in Brisbane.
"I just tried to enjoy to play on the center court again, so I just tried to do my best," Seppi said in a postmatch on-court interview with ESPN. "It was one of my best matches, for sure, or else I couldn't win against Roger. It was fun to play in front of a full stadium."
Federer, uncharacteristically, let mini-breaks slip in both tiebreakers, had nine double-faults in the match and was unusually inconsistent.
"I knew how important that second-set tiebreaker was -- clearly that hurt, losing that one," Federer said. "It just broke me to lose that second set. And actually the fourth, I should win it, too. Just a brutal couple of sets to lose there. The end wasn't pretty."
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. This was his earliest exit in Australia since 2001, when he also lost in the third round.
"I had to believe that I could win," said Seppi, who explained that 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."
Federer, 33, walked over to Seppi's side of the net to shake his hand after the match, and applauded the crowd before he left the arena with his head lowered.
It was only the second time in his last 43 Grand Slam tournaments that the Swiss star failed to at least reach the fourth round.
Federer fell to 1-6 in his career at the Australian Open when falling behind two sets to none. His only win came in the 2009 round of 16 against Tomas Berdych, who earlier Friday became the first men's player to advance to the fourth round when the No. 7 seed beat Viktor Troicki 6-4, 6-3, 6-4.
Seppi will almost certainly get another match in Rod Laver Arena for his fourth-round meeting with Australian teenager Nick Kyrgios, who shrugged off concern over a nosebleed to beat Malek Jaziri of Tunisia 6-3, 7-6 (6), 6-1.
On Wednesday, Nadal needed five sets and 4 hours, 12 minutes to beat American qualifier Tim Smyczek. Ahead of the tournament, Nadal insisted he was not match-fit in the wake of a right wrist injury and appendix surgery that sidelined him for much of the last half of 2014.
Nadal looked in strong form Friday, however, breaking Sela's serve in the opening game of the 2 hour, 4-minute match and advancing to a fourth-rounder against Kevin Anderson of South Africa.
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.
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 to Federer in 2010.
Most of the squandered match points came in the penultimate game, when Troicki held serve. Berdych clinched it with an ace.
"It looks not very nice on the paper -- mostly, all of them on a big first serve," Berdych said. "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."
Information from The Associated Press was used in this report.