De Minaur, Australia’s top-ranked male player, beat Uruguayan Pablo Cuevas 6-3, 6-3, 7-5 after Kokkinakis played out the longest match of the tournament so far.
On the comeback trail from repeated injuries and illness, the world number 267 scored his first Australian Open win since 2015 earlier this week, but fell to Tsitsipas in five sets — 6-7(5/7), 6-4, 6-1, 6-7(5/7), 6-4.
“Thanasi is a great competitor and a great fighter,” Tsitsipas said.
“He’s a great server, has all the weapons from the baseline; despite the difficulty of the match, I really enjoyed being out here showing the world some really high-quality tennis.”
Playing just his fourth major from the past 14 editions, the Australian threatened a massive upset early by winning the first set in a tie break, but Tsitsipas reasserted his dominance with power and precision off both wings over the next three sets.
But Kokkinakis, despite being in a seemingly impossible position while serving at 4-5 in the fourth, refused to be put away as he saved a match point and won a six-deuce game, letting out a scream of relief after getting to 5-5.
Tsitsipas held to love in the next game but could not get on top of Kokkinakis’s serve, with another love hold sending the match to a fourth-set tie break.
Kokkinakis jumped out to a 5-1 lead in the breaker, Tsitsipas hit back to reach 5-5, before Kokkinakis took the set to force a deciding fifth.
“Give me something now,” he called into the crowd, which included Nick Kyrgios, with whom Kokkinakis was supposed to be playing doubles in the night session.
Instead he was locked in a battle with one of the best players in the world, and nothing was coming easy against the two-time major semi-finalist.
Kokkinakis immediately had to fight off two break points in the first game of the decider, but the ultimate test came two games later.
At 1-1, the third game of the set lasted more than 12 minutes and featured seven deuces and two Tsitsipas breakpoints. But again Kokkinakis was up to the task, grimacing through some apparent leg pain as he rescued yet another game from the brink.
The story was not the same two games later, as Tsitsipas finally made good on his threat to break the Kokkinakis serve, and managed to carry that momentum through to the end of the match.
De Minaur to face fiery Fognini as more Aussie wildcards knocked out
De Minaur’s match against Cuevas was less of a scrap, although he did have to dig deep in the third and final set.
Having won the first two sets without much ado, he was given a scare in the third when Cuevas broke serve for the first time in the match.
It gave him an immediate chance to serve for the set at 5-3, but de Minaur did not allow him a look at a set point, immediately breaking back and rattling off four successive games to sew up the match.
He will meet Italian Fabio Fognini in the third round, coming off a marathon five-set match, eventually beating compatriot Salvatore Caruso 4-6, 6-2, 2-6, 6-3, 7-6(14/12).
Earlier, Aussie wildcard Alexei Popyrin was knocked out after his own gruelling five-set match, this time ending in defeat to South African Lloyd Harris.
Popyrin was coming off an almost four-hour upset of 13th seed David Goffin when he ran into world number 91 Harris on Thursday afternoon, losing 6-2, 1-6, 6-3, 6-7 (5/7), 6-3.
The pair went set for set throughout the match, but Popyrin’s almost seven hours on court through the first two rounds started to show with some fatigue late in the decider.
He fought through six deuces at 2-3 in the fifth set, but Harris eventually broke on his fourth chance of the game.
Popyrin slowly trudged to his bag to get a new racket and it was obvious he did not have the energy left in his legs to fight back again.
Harris held serve to love to move to 5-2 and conserved energy through the next game before serving out the match just as the clock ticked over into the fourth hour of the match.
The second-round exit is actually 113th-ranked Popyrin’s worst result in Melbourne since 2018, having reached the third round for the previous two years, while Harris has reached the third round of a slam for the first time.
The tournament of fellow Australian wildcard Chris O’Connell ended in more straightforward fashion, losing to Moldova’s Radu Albot 6-2, 7-5, 7-6(10/8).