Jones tied Dustin Johnson and Gary Woodland for the lowest third-round score at TPC San Antonio, where gusty winds again forced much of the field over par. The Aussie jumped 35 spots in the standings and will begin the final round at even par, tied for 12th and nine shots behind Jimmy Walker.
Jones made five birdies against just one bogey and needed only 26 putts to complete his round. He entered the week at No. 62 in the world rankings and likely needs a top-four finish to move inside the top 50 and earn a trip to Augusta National.
Jones is no stranger to last-minute Masters bids. Last year he topped Matt Kuchar in a playoff at the Shell Houston Open to earn his first PGA Tour win and the final spot in the field for the season's first major. His round continued a strong run of form, as he is now in position for a fourth straight top-15 finish after a solo third-place result last week at the Arnold Palmer Invitational.
While Jones made a move in the third round, other players near the top-50 bubble were unable to keep pace. Entering the week at No. 52, Marc Warren likely needed a top-18 finish to qualify for his first Masters but will begin the final round in a tie for 54th after a Saturday 75, while Harris English dropped into a tie for 33rd after a double bogey on his final hole of the day. English started the week at No. 53 and will likely need a top-seven finish to earn a Masters invite.