The opening 10 games of the first set remained on serve, with Kyrgios' powerful serve once again a force to be reckoned with.
At 5-5, Kyrgios threw his racquet onto the court in frustration following an unforced error on his backhand. Soon after, Kokkinakis was awarded a time violation for taking too long between his serves.
But the Aussies held their nerve, with a well-directed forehand sending the opening set to a tiebreak. The Special Ks found themselves with three set points in the tiebreak, but they only needed two to take the opener on Rod Laver Arena.
Momentum was firmly in favour of the Australian when the second set got underway, with the Special Ks immediately clinching three break points at 1-0.
The Aussie duo couldn't convert the three chances into a break, but even though the game went to deuce, they showed their class to take a 2-0 lead regardless.
The pressure started to get to Kyrgios at 4-2, with the Aussie screaming at the chair umpire when a couple of serves were called as lets.
Not long after, he yelled at a group of spectators who were making noise while he was serving, throwing a tennis ball into the wall.
"When are you going to control the crowd, bro?" Kyrgios screamed at the chair umpire.
Kyrgios and Kokkinakis managed to save two break points, but when their rivals put the second set back on serve at 4-4, the 26-year-old destroyed his racquet by viciously throwing it onto the court.
The Special Ks suddenly had two match points at 5-4 up, and Kokkinakis secured the stunning victory with a well-placed lofted shot.
The Aussie pair clumsily embraced on the baseline after securing the win as the Melbourne crowd went berserk.
"I've played a lot of singles matches around the globe with great atmospheres. This week playing with Thanasi in front of you. Nothing beats this. It's insane," Kyrgios said after the victory.
Meanwhile, over on Margaret Court Arena, Australian pair Matthew Ebden and Max Purcell defeated the No. 2 seeds Rajeev Ram and Joe Salisbury in straight sets to qualify for the men's doubles final.
It's been 42 years since the last All-Australian men's doubles final at the Australian Open.