The 19-year-old dispatched his opponent 6-4 7-6 (7-2) 6-4 in just under two hours to set up a meeting with veteran Spaniard Tommy Robredo.
Winning 51 out of the 59 points on his first serve, Kyrgios' delivery was devastating as he hit 41 winners to Seppi's 28.
The first set was claimed as Seppi faulted in the 10th game but the Italian took it up to Kyrgios in the second set.
After saving two break points at 5-6, Kyrgios excelled in the tie breaker to break the deadlock comfortably.
Kyrgios again saved two break points early in the third set before closing out the match after breaking Seppi in the fifth game.
In other Australian results, Casey Dellacqua reached the US Open third round for the first time as she recovered to eliminate Chinese qualifier Qiang Wang 4-6 6-4 6-2.
With eighth-seed Serbian Ana Ivanovic eliminated, Dellacqua will now face unseeded Czech Karolina Pliskova in a golden chance to go deep in the tournament.
The news wasn't as good for Sam Stosur as she was dumped out by Estonian Kaia Kanepi 3-6 6-3 7-6 (10-8) while Matt Ebden lost 6-1 6-3 6-4 to Argentina's Leonardo Mayer.
Winning 51 out of the 59 points on his first serve, Kyrgios' delivery was devastating as he hit 41 winners to Seppi's 28.
The first set was claimed as Seppi faulted in the 10th game but the Italian took it up to Kyrgios in the second set.
After saving two break points at 5-6, Kyrgios excelled in the tie breaker to break the deadlock comfortably.
Kyrgios again saved two break points early in the third set before closing out the match after breaking Seppi in the fifth game.
In other Australian results, Casey Dellacqua reached the US Open third round for the first time as she recovered to eliminate Chinese qualifier Qiang Wang 4-6 6-4 6-2.
With eighth-seed Serbian Ana Ivanovic eliminated, Dellacqua will now face unseeded Czech Karolina Pliskova in a golden chance to go deep in the tournament.
The news wasn't as good for Sam Stosur as she was dumped out by Estonian Kaia Kanepi 3-6 6-3 7-6 (10-8) while Matt Ebden lost 6-1 6-3 6-4 to Argentina's Leonardo Mayer.