Federer lost to the Italian at the Australian Open in January but allowed no such repeat as he lost just one service game and needed 82 minutes to beat Seppi and advance to fourth round.
Rafa Nadal also advanced with a sloppy triumph over American Donald Young 6-4 6-2.
Nadal, a three-time champion at Indian Wells, looked out of sorts in the opening set slamming an easy overhead into the net to give Young an early break and then later double-faulting to hand over another.
But the 47th ranked Young was no better at finding the target saving just two of eight break points as a fist-pumping Nadal walked off Stadium court at the Indian Wells Tennis Garden with the victory.
While the opening set was a comedy of unforced errors the second saw Nadal flash some of his top form as he raced to a 5-1 lead closing out the match in a tidy 80 minutes.
"It's true that I had a few mistakes. I was able to find solutions," Nadal told reporters. "I've played a lot of good tournaments here, good results.
"I am confident and I hope that tomorrow I can play a good match."
Ninth seeded Czech Tomas Berdych had earlier kicked off another sunny day of action with a straight-forward 6-4 6-2 win over American Steve Johnson.
Jack Sock, however, will carry the American flag into the round of 16 after rallying past 15th seeded Spaniard Roberto Bautista Agut 3-6 6-3 6-2.
France's 13th seed Gilles Simon scored a comfortable 6-2 7-5 victory over German qualifier Michael Berrer while Czech Lukas Rosol was a 6-4 6-7 (4) 7-6 (3) winner over Dutchman Robin Haase, while Spain's Tommy Robredo beat 11th seed Grigor Dimitrov 6-4 1-6 7-5 in the final match to end.
(Reporting by Steve Keating in Toronto and Jahmal Corner in Los Angeles; Editing by Greg Stutchbury)
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