The 28-year-old South Australian eventually triumphed 4-6 5-7 7-6(9) 6-4 6-4, more than 24 hours after the match began, to record his biggest Grand Slam victory in nine years.
“Stoked with that win and happy with how I performed,” Kokkinakis said.
“I took on the big moments today and played the right way.”
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Auger-Aliassime almost closed out a straight-sets victory on Tuesday evening, only for Kokkinakis to save four match points in a tense third-set tiebreak played in fading light.
When the match resumed on Wednesday early in the fourth set, it was Kokkinakis who struck first. He raced to a 5-3 lead, before inclement weather forced the players off court once again.
After pushing the match into a deciding set on return, Kokkinakis charged home to complete a memorable victory after four hours and 38 minutes on court.
“Grass hasn’t been my best surface, but I actually feel like I’m playing some good tennis,” Kokkinakis acknowledged after recording the second main-draw win of his career at Wimbledon.
This is Kokkinakis’ fourth five-set victory on the Grand Slam stage this season and his first top-20 win in a major tournament since upsetting world No.13 Ernests Gulbis as a teenage wildcard at Australian Open 2015.
Kokkinakis’ progression also means six Australian men featured in the second round, matching the most to reach this stage at Wimbledon in the past 24 years.
French qualifier Lucas Pouille, a Wimbledon quarterfinalist in 2016, now awaits in the next round.