Momentum shifted firmly in feisty Cibulkova’s favour in the third set when she broke to take a 4-2 lead and held for 5-2.
The Slovakian fell to the ground and let out a scream when Kerber sent a backhand wide to end a quality match between two of the game’s premier counter-punchers.
The speedy 5 foot 3 inch Cibulkova was strongest in the longer rallies, nimbly moving across the court to extend points during the two-hour 13 minute affair at Louis Armstrong Stadium.
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The pair split sets in an evenly matched fight and began the third with routine holds but Cibulkova drew first blood by breaking Kerber's serve to take a 3-1 lead.
An energised Kerber struck back to break in the next game and close the gap but the comeback was short-lived as Cibulkova broke again and comfortably held for the rest of the match.
"I had my chances, but I couldn't take them, especially in the third set," Kerber told reporters. "She hit the balls really well and played the winners when she had to. I think that was the difference in the match today."
Cibulkova said that after losing to Kerber twice this year, in June at the Eastborne International and in January at the Sydney International, she adjusted her approach to the match.
"We had to change something, and I think we had the great tactic with my coach, and I was able to do it," Cibulkova told reporters. "Of course, I was aggressive going for my forehand, going for my shots. Just overall everything was working."
Cibulkova faces last year's U.S. Open runner-up, American Madison Keys, in the fourth round. Keys leads Cibulkova 4-0 in head-to-head meetings.
Kerber, who won Wimbledon in July, was the latest favourite to be knocked out of the women's singles at Flushing Meadows after top seed Simona Halep and second seed Caroline Wozniacki.
(Additional reporting by Amy Tennery; Editing by Ken Ferris)
