Federer proved a cut above and beat Fritz 6-2, 7-5, 6-2, while Nadal enjoyed a similarly simple outing against De Minaur, who struggled to keep pace with his second-seed superior in a straight-sets loss.
Stefanos Tsitsipas will attempt to knock Federer out of the running in the round of 16 after he defeated Nikoloz Basilashvili 6-3, 3-6, 7-6 (7), 6-4, and unseeded Tomas Berdych beat Diego Schwartzman 5-7, 6-3, 7-5, 6-4.
Sixth seed Marin Cilic emerged on top of one of the best comebacks we're likely to see at this Australian Open, beating Fernando Verdasco 4-6, 3-6, 6-1, 7-6 (8), 6-3 in a match lasting four hours and 20 minutes.
Maria Sharapova forced a shock in the women's singles and reiterated her intent to win a first major since 2014 by upsetting defending champion Caroline Wozniacki 6-4, 4-6, 6-3. No. 2 Angelique Kerber was less surprising as she ran to an imperious 6-1, 6-0 win over Kimberly Birrell.
There was a shock lower down the pecking order, too, as 17-year-old Amanda Anisimova became the first player born in the 2000s to book a Grand Slam fourth-round spot by beating 11th seed Aryna Sabalenka 6-3, 6-2.
Fifth seed Sloane Stephens will join them in the fourth round and secured her place with a 7-6 (6), 7-6 (5) win over No. 31 seed Petra Martic, reaching this stage of the competition for the first time since 2014.
(14) Stefanos Tsitsipas bt. (19) Nikoloz Basilashvili: 6-3, 3-6, 7-6 (7), 6-4
Tomas Berdych bt. (18) Diego Schwarzman: 5-7, 6-3, 7-5, 6-4
(3) Roger Federer bt. Taylor Fritz: 6-2, 7-5, 6-2
(20) Grigor Dimitrov bt. Thomas Fabbiano: 7-6 (5), 6-4, 6-4
Frances Tiafoe bt. Andreas Seppi: 6-7 (3), 6-3, 4-6, 6-4, 6-3
(22) Roberto Bautista Agut bt. Karen Khachanov: 6-4, 7-5, 6-4
(2) Rafael Nadal bt. Alex de Minaur: 6-1, 6-2, 6-4
(6) Marin Cilic bt. (26) Fernando Verdasco: 4-6, 3-6, 6-1, 7-6 (8), 6-3
(15) Ashleigh Barty bt. Maria Sakkari: 7-5, 6-1
Amanda Anisimova bt. (11) Aryna Sabalenka: 6-3, 6-2
Anastasia Pavlyuchenkova bt. Aliaksandra Sasnovich: 6-0, 6-3
(5) Sloane Stephens bt. (31) Petra Martic: 7-6 (6), 7-6 (5)
(30) Maria Sharapova bt. (3) Carolina Wozniacki: 6-4, 4-6, 6-3
(8) Petra Kvitova bt. Belinda Bencic: 6-1, 6-4
Danielle Collins bt. (19) Carolina Garcia: 6-3, 6-2
(2) Angelique Kerber bt. Kimberly Birrell: 6-1, 6-0
Visit the Australian Open website to see results in full.
Federer may be set to turn 38 in August, but the Swiss superstar continued to show great stamina as he beat Fritz on Friday, and he is still yet to drop a set at the Australian Open this year.
The third seed failed to face so much as a break point and was the clear superior over the course of their clash, while Federer took five of the nine break opportunities he had, per the official Australian Open website.
Fritz found fortune at the net in patches, but it was only in their second set that Federer showed any signs of creaking in what was a fairly pristine performance:
The same could be said for Nadal in his win over De Minaur, a 19-year-old opponent who showcased some endearing qualities in the face of such irrepressible talent.
The Australian was soundly beaten in the end but never looked like giving up the fight altogether, best summarised in a climactic final game that saw him save five match points before he finally broke.
Tsitsipas should prove a more worthy foe for Federer in the fifth round and presents the world No. 3 his first seeded opponent in Melbourne this year, coming off the back of a morale-boosting victory of his own.
The Greek prospect and 19th seed Basilashvili were split by narrow margins over four sets, as Tsitsipas reached the last 16 of a Grand Slam for the second time in his career (first at the Australian Open).
While those stars enjoyed more straightforward wins, Cilic took the long route in a five-set war against Verdasco, which saw the Croat come back from two sets and two match points down to beating the No. 26 seed.
Cilic lost a crushing final to Federer in the final of last year's contest—just the second time he'd ever made it past the fourth round in Melbourne—but he showed sensational grit to at least attempt competing again:
Grigor Dimitrov was the favourite to beat Thomas Fabbiano and pushed the Italian to one side to set up a fourth-round clash opposite Frances Tiafoe, who ground out a hard-fought win against Andreas Seppi.
Federer still has a chance to retain his crown in Melbourne, but the same can no longer be said for women's title-holder Wozniacki after Sharapova sent her out, via Eurosport UK:
Sharapova has made it to the fourth round of successive majors for the first time since 2015 with that win, which saw her advance despite committing more than twice the number of unforced errors as Wozniacki (46 to 21).
Hers wasn't the only shock, either, as 11th seed Sabalenka tumbled out of the competition at the hands of teenager Anisimova, who was well worthy of her straight-sets win despite the surprise:
Her range of shots across the court and the ability to perform under pressure meant she was unbroken by her seeded foe, and she'll next hope to upset eighth seed Petra Kvitova, who beat Belinda Bencic.
Anisimova's American compatriot Stephens also progressed with a straight-sets victory of her own, although the 7-6 (6), 7-6 (5) beating of Martic looked a lot closer in terms of competition:
Birrell stood little chance of impeding Kerber, who made light work of the Australian, born in Dusseldorf. The No. 2 seed retains hope of extending her fine run of form at the Australian Open after reaching at least the final four in two of the past three tournaments, winning the crown in 2016.
Kerber will face Danielle Collins, who surprised 19th seed Caroline Garcia with a 6-3, 6-2 clean sweep and could help Americans make up more than a quarter of the round-of-16 draw.