It was the first match on the ATP tour in 167 days for Kyrgios, while Kokkinakis played for the first time since suffering a pectoral injury in January 2025, as the pair beat Matthew Ebden and Rajeev Ram 5-7, 6-4, 10-8.
"I'm about to tear up," an emotional Kokkinakis said in the post-match interview.
"It's crazy. I haven't played a match in 12 months... I underwent surgery a year ago with no guarantee I would be back playing. So it's been a long year, a challenging one a lot of times, where I thought the game was done for me. So I chipped away at it."
Kyrgios and Kokkinakis won the men's doubles title in the Australian Open 2022. The pair reunited ahead of last year's Australian Open, but their campaign ended in the first round due to Kokkinakis's injury.
"It's doubles but it means everything. This is a good stepping stone," Kokkinakis added.
The Australian duo will face French sixth seeds Sadio Doumbia and Fabien Reboul in the second round.