After the fancied Jordan Thompson got knocked out tamely and Aleksandar Vukic felt the brilliance of champion Carlos Alcaraz in second-round defeats, Kokkinakis completed his two-day, first-round contest against one-time Canadian wonder boy Auger-Aliassime with a 4-6 5-7 7-6 (11-9) 6-4 6-4 triumph.
The four-hour 38-minute duel followed two epic five-set triumphs for Adelaide's marathon man at the recent French Open.
He has now gone the distance in five of his six grand-slam matches this year.
"I'd rather not keep playing five-setters," Kokkinakis sighed with a rueful smile on court, to much laughter.
"It doesn't help me going deeper into the tournament, that's for sure.
"Thankfully, it is best-of-five, otherwise I wouldn't have won many matches this year."
But this one was particularly satisfying as the 28-year-old had only just returned from injuring his knee when slipping on the grass at Queen's Club recently, and he was proud of how he coped with damp, difficult conditions.
On Tuesday night, the world No.93 had been on the brink of defeat in straight sets with Auger-Aliassime having held four match points in the tie-break.
But Kokkinakis edged the breaker, and after the match was postponed for the day at the start of the fourth, returned to take his chances on Wednesday.
Drizzle twice further held up the match before he prevailed to set up a second-round tie against French qualifier Lucas Pouille on Thursday.
Carlos Alcaraz got a brief scare before outclassing Aleksandar Vukic at Wimbledon. (EPA PHOTO)
Recent Queen's Club star Thompson couldn't cope with the excellence of American Brandon Nakashima, succumbing in three one-sided sets 6-3 6-2 6-2.
Fellow Sydneysider Vukic followed up under the roof of No.1 Court, briefly offering the holder Alcaraz a scare as he served for the first set on his showcourt debut.
However, the Spanish star moved into an unstoppable higher gear to triumph 7-6 (7-5) 6-2 6-2.
The 30-year-old Thompson, in the middle of a breakthrough season in which he lifted his first ATP title, simply couldn't back up his first-round comeback victory over five sets against Russian Pavel Kotov.
Thompson, who's no stranger to five-set arm wrestles like Kokkinakis, couldn't lay a glove on the man he fought back from two sets against to beat in last year's first round.
Nakashima was dominant in every department as world No.40 Thompson, who only narrowly missed out on seeding at Wimbledon, appeared powerless, unable to convert his measly two break points as the American cracked 37 winners.
"He played incredible," shrugged Thompson.
"Nothing's wrong; he just played a great match."
Jordan Thompson was the picture of disappointment during his loss to Brandon Nakashima. (AP PHOTO)
Big-serving Vukic's dream of a grand-slam showcourt date was everything he had imagined - for a set.
The world No.69 reeled off four games in a row to serve for the opener, only for the champion to suddenly start playing like one.
The 28-year-old Vukic is the only Aussie ever to have beaten Alcaraz in the pro ranks, having defeated the then-17-year-old in French Open qualifying four years ago.
"But he was a child then," Vukic said.
Alcaraz the man proved a very different proposition once he got into his stride in the second set, unveiling a panoply of dramatic shot-making to blitz 42 winners and set up a third-round date with Frances Tiafoe.
But Vukic cherished the experience.
"Really cool to be able to compete in a court like that against one of the best players in the world, who will be at the top of the game for a while," he said.
"He was nervous, for sure, for a while, maybe losing his focus.
"That's exactly where I needed him to be, but I didn't capitalise and then he played pretty unstoppably."
