Federer was trying to come from two sets down for the 10th time in his career, most recently at last year's U.S. Open against Gael Monfils.
The 17-time Grand Slam champion hasn't been beaten this early at the Australian Open since 2000, the second year he played here. It was also the unseeded Seppi's first win against Federer in 11 matches.
Third-seeded Simona Halep advanced to the fourth round with a 6-4, 7-5 win over Bethanie Mattek-Sands.
Halep, the 2014 French Open finalist, opened the season by winning the Shenzhen Open in China. She was a quarterfinalist at last year's Australian Open.
Canada's Eugenie Bouchard struggled through a scrappy opening set before getting on top in a 7-5, 6-0 third-round win over Carolina Garcia in a match that featured 10 service breaks..
"Yeah, I don't think it was the prettiest tennis out there," said Bouchard, who reached the semifinals in her first trip here last year and went on to make the semifinals or better at two of the other three majors.
Seventh-seeded Tomas Berdych became the first man to advance to the fourth round when he beat Viktor Troicki, 6-4, 6-3, 6-4, and No. 10 Grigor 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.
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.
In a late Thursday match, two-time Australian champion Victoria Azarenka took out No. 8-seeded Caroline Wozniacki, 6-4, 6-2, to reach the third round.