Cantlay carded a closing 67 to tie Cejka (63) and Kim (66) at nine-under 275, one shot clear of three others after a wild finish in windswept conditions.
Las Vegas resident Cejka had a good chance to win at the first extra hole but his 15-foot par putt caught the edge of the cup and stayed out, while Cantlay had to sink a seven-footer for bogey to stay in it.
The win was the first in 43 starts on tour for the 25-year-old, a former amateur standout who has had to overcome a serious back injury and several other setbacks.
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"It was a grind the last few holes," Cantlay said.
"I had so many lows and all the hard work I did, it's just so different from where I was that it's hard to describe the feeling."
Five players were tied for the lead late in the final round as gusty winds took a heavy toll at the 456-yard par-four 18th.
J.J. Spaun, who started the day tied for the lead, was alone in front at 10-under with two holes left, but finished with consecutive double-bogeys to plunge into a tie for 10th three shots back.
(Reporting by Andrew Both in Tokyo, editing by Gene Cherry/Peter Rutherford)
