Kyrgios, who is the No 15 seed in Ohio, took the first set against the young Croatian in tie-break where he lost just one point.
However, the Australian’s game went to pieces in the second when he appeared to lose focus thanks to an incorrect line call.
Kyrgios, 23, was already 2-0 down and serving at deuce when he ran to the net in an effort to end the point, only for Coric to pass him down the line.
But Kyrgios was furious with the judgement that the ball had landed on, not outside of, the sideline, begging the umpire to overrule it and continuing his rant during changeover after losing the game.
“He can screw up a number of times, nothing happens to him,” Kyrgios said of the offending line judge.
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“It’s continual, like every time I play with him.”
The fiery world No 18 then began talking to the crowd during the match out of frustration with the situation as the second set slipped away.
“Where the hell do you find these guys?” Kyrgios added.
“You want to be a referee? You’re all eligible.”
He also said: “You’ll never see a bigger tank than the next three games.”
And Kyrgios was true to his promise, losing the second set 6-0 in just 25 minutes to force a decider for a place in the third round.
But he rediscovered his best form when it mattered, taking the only break point of the set in the fourth game and then serving the match out to love.
And Kyrgios stood by his decision to play poorly in the second set as it allowed him to conserve energy ahead of the third.
“I knew I was always going to compete in the third set,” Kyrgios said afterwards.
“I competed too hard in the first set to sort of just let the match slip and not give myself a chance to win, at least.
“The second set, when I was 4-0 down, I knew there was no real point going out there and competing and obviously waste energy trying to battle back.
“I knew at 4-0, if I lost the set 6-0, I was going to be serving first in the third set.
“I think I carried a lot of momentum from the first game, and it ended up being a smart move.”
Kyrgios will either Hyeon Chung or Juan Martin Del Potro for a place in the quarter-finals.