LA QUINTA, Calif.—Harrison Frazar shot a 59 in the fourth round of the PGA Tour qualifying tournament Saturday, the first player in eight years to hit golf’s magic number at Q-school.

Frazar, winless in 300 starts during his PGA Tour career, had a 30 on the front nine of the Nicklaus Tournament course at PGA West, then ran off seven consecutive birdies from the 11th hole. He knocked in a 35-foot birdie putt on the 17th to reach 13 under, and he had a birdie putt on the 18th that came up just short.

“The 59 is nice,” Frazar said. “That is something I will always have wit...

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