Five long years since his last appearance at the All England Club, Kokkinakis continued his 2022 renaissance with a watershed 7-6 (7-5) 6-2 7-5 victory over Poland's Kamil Majchrzak on Monday.
After two previous first-round defeats, plus two unsuccessful qualifying campaigns, the 26-year-old is finally savouring his maiden win on London's hallowed grass courts.
And the rich reward is a show-court showdown on Wednesday with Djokovic, the 20-times grand slam champion chasing a seventh Wimbledon crown - and fourth straight.
Djokovic earlier opened his title bid with a scratchy 6-3 3-6 6-3 6-4 victory over Korean Soonwoo Kwon under a closed roof on centre court.
Kokkinakis, who also landed his maiden ATP title in January in Adelaide, was among eight Australians scheduled for action on a rain-marred day one.
Brave Sydney qualifier Max Purcell lost a three-hour, 53-minute epic against Frenchman Adrian Mannarino.
Playing with a lost big toe nail on his right foot, Purcell rallied back from two sets down to force a decider, only to succumb 6-3 7-6 (7-0) 4-6 4-6 6-4 in his first-ever five-setter.
James Duckworth and John Millman were also set for men's action.
Duckworth had a dream centre-court date with Britain's two-time Wimbledon champion Andy Murray, while Millman was due to face Serb Miomir Kecmanovic.
Women's wildcard Daria Saville, up against Viktoriya Tomova, plus qualifying trio Zoe Hives, Astra Sharma and Maddison Inglis were also hoping to hit the courts after two rain delays.
Hives plays fifth seed Maria Sakkari, Sharma meets Tatjana Maria and Inglis faces Dalma Galfi.