Kokkinakis had waited for eight long injury-interrupted years to reach the third round of another grand slam after reaching the last-32 at Roland Garros as a teenager and was left clearly emotional at finally repeating the dose with his monumental effort on Wednesday.
On a gusty Court Simonne Mathieu, faced by a packed house all cheering for their Swiss favourite, Kokkinakis eventually broke the dogged 2015 champion, winning 3-6 7-5 6-3 6-7 (4-7) 6-3 to become the first Australian to make the third round this year.
In doing so, the man from Adelaide went a huge way to exorcising some agonising near-misses, headed by his near six-hour loss to another never-say-die champ Andy Murray at the Australian Open.
He even had to go through the agony of Wawrinka saving four match points in the final game before sealing the win.
Nick Kyrgios, who'd once famously taunted Wawrinka during a match in Montreal by telling him that his friend Kokkinakis had once slept with the Swiss's girlfriend, had built this contest up as a real "popcorn match" - and he wasn't wrong as a breathtaking four hour 38 minute contest unfolded.
The Kokkinakis win was the perfect pick-me-up for the Aussie challenge in Paris after Storm Hunter's own chance of a breakthrough triumph on the same court over Ukraine's comeback star Elina Svitolina had earlier blown out after a dazzling start as she went down 2-6 6-3 6-1.
And Hunter's fellow Queenslander Jason Kubler also departed in the second round, beaten by the swashbuckling Italian Fabio Fognini 6-4 7-6 (7-5) 6-2.
Up against an even more popular clay-court veteran, it had looked for a while as if Adelaide's Kokkinakis also might find the 38-year-old Wawrinka too hot to handle in the battle between two warriors finding fresh life in their careers after being put through the injury mill.
Wawrinka, who'd come through a thrilling five-set win in his opener against Albert Ramos-Vinolas, was gifted the only break of the first set with a Kokkinakis double fault on break point at 4-3.
When the Australian went 4-2 down in the second, it looked really ominous but Kokkinakis started to move the Swiss around the court more and his increased aggression and weight of shot saw him began to bully Wawrinka.
He looked in control at the start of the fourth once he'd staved off a host of break chances but the relentless Wawrinka took the stanza to a tie-break and then watched Kokkinakis play a shocker, dishing up five straight unforced errors as the Swiss levelled affairs.
But Wawrinka's energy levels seemed to be dwindling as Kokkinakis reeled off four straight games and, even though he rallied with a break and saved five match points, the Australian prevented the Swiss earning a record 12th five-set win at Roland Garros.
Earlier, Hunter had briefly upgraded from Storm to 'Hurricane' before her gale of winners subsided and her chance of her greatest win against the former world No.3 Svitolina was simply blown away.
The quality Ukrainian, whose successful, politically-charged return to the circuit after giving birth to a daughter has been a big talking point at the Paris grand slam, eventually proved to be a class above.
"I'm definitely not deflated," said a proud Hunter, who'd completely dominated her illustrious opponent early on behind a cracking forehand that produced 11 first-stanza winners.Â
Out on court 6, world No.69 Kubler, the last Aussie man standing at last year's Roland Garros, found the mercurial 36-year-old Fognini, who's dropped to 130 in the rankings, to be on one of his more focused days as the Italian gave him a bit of a clay-court lesson.
