Claxton, who has been playing on minor golf circuits since finishing his collegiate career at Auburn almost a decade ago, shot a 2-under 70 to finish 36 holes in 10-under 134.
The second day of the six-round tournament was plagued by the high winds that have swept across Southern California. There were 58 sub-70 rounds Wednesday but only 13 Thursday.
The 171 players in the final stage of the qualifying tournament take turns playing both the La Quinta Nicklaus Tournament Course and the PGA West TPC Stadium Course. The top 25 players after six rounds earn playing privileges on the PGA Tour next year.
Matt Jones and Harris English shared second place at 135. Billy Hurley III was alone in fourth at 136.
Hurley has already earned his tour card for 2012 by finishing 25th on the Nationwide Tour money list, but he is trying to improve his position on the regular circuit. He attended the U.S. Naval Academy and played on the 2005 American Walker Cup team before fulfilling his five-year military obligation.
This year's season on the Nationwide Tour was his first as a competitive professional golfer.
Celebrity Families of 2014 [PHOTOS]