Kokkinakis overcame an explosive first-set exchange with the chair umpire and the loss of the second set to upset the world No.6 with a sublime serving display on Wednesday night.
The South Australian crowd favourite rocketed down 17 aces to storm into the quarter-finals with a 6-4 3-6 6-3 win before a sellout crowd at Memorial Drive.
Kokkinakis will play Miomir Kecmanovic for a place in the last four after the Serb eliminated fellow Australian Jason Kubler 5-7 7-6 (7-1) 6-4.
Compatriot John Millman will turn his attention to an Australian Open wildcard crack after bowing out earlier in the second round on Wednesday.
The 33-year-old, who had a rough year on tour in 2022, was ousted 6-3 6-3 by world No.32 Alejandro Davidovich Fokina.
Millman, ranked No.148 in the world, had battled through qualifying to reach the main draw of Adelaide and knocked off world No.38 Albert Ramos-Vinolas, another Spaniard, in the first round.
He vented his frustration at the chair umpire after Davidovich Fokina won the first set following a line-call challenge.
Davidovich Fokina successfully challenged a shot by Millman that was originally called in.
Millman thought his opponent, who played and missed the next shot, took too long to challenge.
"He goes for the winner, misses it and then says challenge. That's where you have to go 'no, it's too late'," Millman told the umpire.
He responded by breaking in the opening game of the second set but Davidovich Fokina broke straight back and won the next three games.
Millman, who notched a win over Roger Federer at the 2018 US Open and has been as high as No.33 in the world, dropped down the rankings last season after a bizarre eye injury in February.
Playing in Mexico, a ball deflected off his racquet and struck him in the eye scratching his cornea.
Davidovich Fokina will meet either compatriot and fourth seed Roberto Bautista Agut or Dutchman Robin Hasse in the quarter-finals.
14°C