The 23-year old advances to a major quarterfinal for the first time in his career and he will face third seed Grigor Dimitrov for a spot in the semifinals.
Seppi edges first set in tie-breaker
The server dominated the early stages of the match with Seppi providing the first test, pushing Edmund to deuce before a cracking forehand brought the Brit through the game to level at 3-3.
The next service game for Edmund proved to be more troublesome as the Italian had five break points, all saved with some solid serving by the 23-year old and unforced errors from his veteran opponent.
Edmund was making virtually no impression on the Seppi serve and after the Italian held easily again for a 6-5 lead, the trainer paid the Brit a visit for treatment to his right shoulder, perhaps feeling the wear and tear of the longest week of his career.
After overcoming a 15-30 deficit on serve to force a tiebreaker, Edmund began leaked errors off the ground, three of them eventually giving Seppi a 5-4 lead before the Italian snatched the breaker with a pair of winners, his forehand on set point finding the mark to wrap up the opening set.
Edmund levels match with close second set victory
The Brit was given a small opening in Seppi's first service game of the second set, building a 0-30 lead, but more untimely errors and an ace allowed the Italian to hold.
The veteran was kicking it into high-gear and he broke in the next game with a combination of more errors from the Brit and superbly struck winners.
Edmund needed a response and he led 0-40, only to see Seppi peg him back on all three chances. A fourth break chance and a forehand winner put the Brit back on serve at 2-2.
Both players would steady themselves and with Edmund in the lead at 6-5, he was regularly pressuring the Italian's serve and he made the breakthrough, a pair of net cords, the second guiding Seppi's groundstroke wide, aiding the 23-year old's cause to level the match at one set all.
Edmund dominates the third set
Carrying the momentum over to the third set, it was Edmund who jumped out on top as Seppi's suddenly failing serve was breached again, a thumping winner struck by the Brit off a second serve for a 2-0 lead.
It was all going Edmund's way now and he was overpowering the Italian in every department, his service games going by in the blink of an eye to build a 5-2 advantage.
Going in for the kill, Edmund stormed into a 15-40 lead and when a soft second serve sat up to be hit, the Brit made no mistake and he wrapped up the set in style, taking a two sets to one lead.
Edmund closes strong to advance to quarterfinals
Three games in, three holds. After Edmund held for a 2-1 lead, Seppi called the trainer for a rubdown on his shoulder, the effects of a long week taking its toll on the 33-year old.
A bit ragged himself, the Brit struggles along to hold, Seppi's groundstroke suddenly deserting him. A foot fault at deuce in the next game puts the Italian in a precarious position and after protesting to the umpire, holds.
Edmund sought to close strong and some massive groundstroke winners give him the break at 5-3. Serving for the match, he gets to 40-15 and a perfectly angled wide serve seals the match and sends the 23-year old into his maiden Slam quarterfinal.
Edmund has dug deep this fortnight, rallying three times from a set down. With Andy Murray sidelined, this is his chance to step into the spotlight and he's taken advantage of that as well as his draw opening up. He's the first Brit outside of Murray to reach the last eight in Melbourne since John Lloyd in 1985 and with his weapons and little to no pressure on him against Dimitrov, he has every chance to upset the Bulgarian.
Commiserations to Seppi. He's 33 now. A solid veteran throughout his career, he may never get a better opportunity to reach a Slam quarterfinal. Up a set and a break, he wilted probably due to fatigue and the powerful nature of Edmund's game. It's good to see the Italian playing well again and he'll look to use this momentum he gained in Melbourne to try and make it back onto the