The 'Special Ks' fought their way into the quarterfinals with a 6-4, 4-6, 6-4 victory over 15th seeds Ariel Behar and Gonzalo Escobar in front of a full house at Kia Arena on Sunday, having already upset top-ranked Croatian duo Nikola Mektic and Mate Pavic in the second round.
The Australians' form and on-court showmanship have reignited interest in the men's doubles tournament at Melbourne Park, with patriotic and often boisterous crowds flocking to their matches.
It could have further consequences, with the Kyrgios-Kokkinakis combination shaping as a potential winner for Australia's Davis Cup qualifier against Hungary in Sydney in early March.
Kyrgios has previously thrived in singles on John Cain Arena and he and Kokkinakis have relished their hectic doubles crowds.
"You can't not get up for matches like this," Kokkinakis said.
"Tell Craig (Tiley) to keep scheduling us out here. This atmosphere is nuts."
"We're winning it," Kyrgios said.
"I definitely think we've got a good shot of winning this.
"We're locked in."
The pair have also attracted attention off the court.
Kyrgios on Saturday claimed the trainer of Pavic and Mektic had threatened to fight him in the players' gym after Friday's upset.
On Sunday, Kokkinakis and Kyrgios got off to a red-hot start, combining for nine unanswered aces and 14 winners to claim the first set.
Behar and Escobar hit back to claim the second set as a frustrated Kyrgios got a ball abuse warning for smashing one out of Kia Arena in the second set, while he later threw his racquet to the ground.
But the Australian duo were able to reset and snatched the crucial break on Escobar's serve to take a 3-2 lead in the decider.
Kyrgios served for the match and pulled off two aces and a delightful lob to earn three match points, with Kokkinakis converting the first via a lovely volley winner.
"We both lost early in singles but to come out here and have this atmosphere pretty much for a doubles match is insane," Kyrgios said.
"You don't get it anywhere else in the world."