The 20-year-old came from behind to win 6-7 (11), 7-6 (3), 7-5, 7-6 (5) in a thrilling contest in Melbourne.
An aggressive start from Federer forced his opponent to fend off two break points in an eight-minute opening game. The pair rattled through the games at a much quicker pace as the set continued to follow serve, though.
Tsitsipas, who impressively recorded three consecutive holds to love, showed himself to be more than a match for the Swiss maestro:
The inevitable tiebreaker was just as competitive, with both players producing some superb play but struggling to close it out, as Federer's forehand unusually let him down in the key moments.
Federer eventually claimed it after saving three set points, though, and Tsitsipas had every reason to be disappointed with how the final point played out:
The second set continued in much the same fashion, until Federer began to turn the screw again on Tsitsipas' serve. The Greek saved three break points to level the scores at 3-3 before batting back two more in his next service game.
Record's Jose Morgado noted how closely matched the pair have been in their limited dealings with one another:
Tsitsipas struggled to get near the veteran's serve, but he continued to show remarkable resilience as he saved four set points on the way to forcing another tiebreaker.
A pair of unforced errors from Federer either side of a Tsitsipas forehand winner handed the latter three set points, and he took the first to level the match.
Federer's inability to break his opponent continued in the third set, as the Press Association's Eleanor Crooks observed:
A lovely passing winner from Tsitsipas earned him his first break points at 4-4. They came and went as quickly as they'd arrived, but a couple of errors from Federer at 6-5 handed him two set points, which he duly converted.
There was little to separate the pair again in the fourth, as they battled to yet another tiebreaker.
A long forehand from Federer at the crucial moment gave Tsitsipas a match point, and he made no mistake in closing out the match:
The No. 14 seed will face Roberto Bautista Agut in the next round following his triumph over Marin Cilic.