Jones, tied with McNeill for the first-round lead, had a bogey-free morning round to reach 11-under 133 on the wind-swept Trump International course. The Australian is winless on the PGA Tour.
“I’ve been putting really well and chipping unbelievably well,” Jones said. “My ball-striking was much better yesterday. I missed a few greens today.”
The wind increased throughout the day, gusting to 23 mph in the afternoon.
McNeill had 70.
Japanese star Ryo Ishikawa, playing the event for the first time after failing to qualify for the World Golf Championship event at Doral, was four strokes back at 7-under after 67.
NATIONWIDE TOUR: In Santiago, Chile, Paul Haley II shot 8-under-par 64 to take a two-stroke lead over Christopher DeForest at the Chile Classic.
DeForest had 65 in the second round.
Haley is at 13-under 131 at Prince of Wales Country Club.
Augusta’s Scott Parel shot 70 and is four strokes off the pace.