Jones shared the first-round lead with George McNeill at the Trump International Golf Club, and his two-day total of 11-under 133 put him in position for his first PGA Tour victory.
He lost his exempt status last year, but regained it by finishing third at the tour's qualifying tournament.
Jones has put together two solid rounds after struggling in his first three events on the tour this year. He finished in a tie for 40th at one of the tournaments and missed the cut in the other two.
"My putting was terrible last year and that's why I'm in this situation right now," Jones said. "But I actually fixed it last week and it's coming along nicely."