The 17-times grand slam winner lost his first match in 11 meetings with Seppi.
"I just tried to enjoy playing on centre court again," Seppi said after his win. "It's not often you get the chance to play on centre court.
"I just tried to play my best and I did because I was playing Roger.
"You never feel comfortable playing against Roger, but I was focussing on my service game, I didn't have many chances on his serve."
Federer struggled with his game generally, especially his serve and forearm were patchy throughout.
Seppi took advantage of three of his five break points to take a two sets to love lead.
Federer broke in the third game of the third set to eventually win the set 6-4, but Seppi held his never and eventually won the fourth set tiebreaker and will next face either Australian Nick Kyrigos or Tunisia's Malek Jaziri.