Koepka finished three rounds at 15-under-par 198 as he seeks his first-ever PGA Tour title.
George McNeill charged into a share of second place at minus-13 with a sterling round of 9-under 62, matching the course record at CordeValle Golf Club.
He ended the day knotted for second with Jason Kokrak, who carded a 3-under 68.
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