Edmund came from behind to beat Seppi in four sets in Melbourne on Sunday, claiming a 6-7 (4-7) 7-5 6-2 6-3 victory over the Italian.
With Andy Murray missing due to injury and Johanna Konta making an early exit, British hopes were residing in the world number 49, who had shown flashes of talent in Slams but had only ever reached one fourth round: the US Open in 2016.
World number three Dimitrov was tested by Edmund in the Brisbane International this month, the Bulgarian needing to come from a set down to win that quarter-final match.
Edmund broke again at 5-2 with a rasping forehand cross court return victor to put himself within a set of the quarter finals.
It's the British player's first quarterfinal appearance in Melbourne and his best Grand Slam singles result.
Caroline Wozniacki and Elina Svitolina remained on course for a semi-final meeting in the women's tournament after easy wins. My hard work is paying off - just working at everything, my game, on and off the court.
"You want black-and-white evidence to say, yeah, I'm playing well and beating these guys".
Both players continued to remain assured behind their delivery until the 12th game of the second set when Edmund seized on an indifferent service game from Seppi to break the Italian for the second time and level the match at one-set all. I have to believe I'm going to win and believe in my game and stuff.
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"I'm just really focused right now on my side of the court". But it wasn't until he barrelled down a second-serve, 187kph ace - his 25th - at the start of the third that Edmund went ahead in the match for the first time.
But Edmund has a lot of confidence in his game and himself and, having won four matches, does not consider another three to be beyond him. Today I'm happy I switched on a gear and was playing better and better.
"It's not like I have changed my game or anything from a year ago". 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. The 33-year-old had the first set in lockdown, hardly making any errors and striking the ball with flawless timing.
The man who lost tight three-setters time and again on the ATP Tour previous year is now finding a way to win when his back is to the wall.
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. At the beginning of the tournament I wasn't hitting the ball too well. The Brit then rallied, winning 7-5. I played well; he played well.
But he finally faltered in the eighth and Edmund earned the chance to serve for the match.