The Australian defeated his big-serving rival after coming from a set down to take out a 6-7 (5-7) 7-6 (7-5) 7-6 (7-4) win.
Kokkinakis took control of the final set tiebreaker by zooming out to a 3-0 lead before holding his nerve to close it out as Isner, the world No.24, looked increasingly frustrated.
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Narrow margins separated the pair throughout the match, both players winning 18 service games and 111 points apiece.
Kokkinakis’ win sets up an all-Australian quarter-final clash against countryman Aleksandar Vukic after Vukic’s straight-sets win over American foe, Steve Johnson.
Following his win, the 25-year-old gave a unique insight into facing the giant Isner serve, admitting he was playing somewhat of a guessing game at times.
“Playing him is not fun. I’ve had a few frustrating things in life, but that one’s up there for sure,” he said. “You feel like you’re walking side to side.”
“I just had to take my chances, I didn’t in the first set and I thought maybe I had created the most chances in the first set, but I had to keep a clear head.
“It ends up being about, ‘How do I distract him without being an idiot?’. I was trying to stand on the fence, stand close, I don’t know. That’s why he’s so good and [has] been so good for so long.
“I just had to hope he’d miss a first serve, or if he jagged one, somehow return and be really sharp after that.”