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.
In winning, he became only the sixth British man to reach the quarter-finals of the Australian Open in the post-1968 Open Era.
"That's why I'm in the quarter-finals, because every time I step on the court and I'm playing, I believe I'm going to win".
The British number two, speaking after his win over Seppi, said: "It's a good feeling, an interesting match and I didn't think I got off to the best of starts - he was dictating things and I had to change the course of the match".
Edmund had the worst of conditions on Friday, requiring five sets to beat Nikoloz Basilashvili in 40 degree heat, and while Seppi also needed to go the distance against Ivo Karlovic, it's much easier facing a big server in frequently shorter points in longer matches. Shows I'm improving. Also hard work paying off.
Rafael Nadal is a fan of Kyle Edmund’s game
"In the second set I tried to shift the momentum and once I broke him in the last game of the second set I took control of the match". So he will be grateful for his day's recovery for one of the biggest matches of his career so far-against world No3 Grigor Dimitrov, though it was many hours later that the Bulgarian's thrilling encounter with Nick Kyrgios reached its conclusion. "I'm just really focused on my side of the court".
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. "It was a little bit more surprising for me a year ago he lost a lot of close matches". He has a huge serve, huge forehand, and he hits very strong the ball.
It is a message that Dimitrov has increasingly taken to heart in the previous year, and judging from those 12 months, he may manage to "go to all the way" this time-though he has that same formidable challenge in the semis: Nadal.
The third set was all Edmund as Seppi began to tire. He'd been hitting 205kph at the higher end of his serving efforts, averaging 187kph, numbers in keeping with his tournament averages, mid-range among the speed merchants but potent enough. He was bullying Seppi with his sheer weight of shot, and eventually completed his 6-7, 7-5, 6-2, 6-3 victory in 2hr 57min. I played well; he played well.
"The most important thing for me is after not playing anything before here I am able to be in the quarter-finals".
He will play third-seeded Bulgarian Grigor Dimitrov next and sees no reason why he can not make further progress. Up a set and a break, he wilted probably due to fatigue and the powerful nature of Edmund's game.
Philly is a finalist for Amazon HQ2. What comes next?
Apple on Wednesday announced that it planned to establish a new campus, the location of which it would name later in the year. And there's a clear cluster around D.C., including Washington itself; Montgomery County, Maryland; and Northern Virginia.