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.
"It started to kick up maybe around the eighth, ninth hole, but compared to yesterday, I didn't really feel it," Jones said. "Growing up in Australia, we're used to playing in the wind. It's nothing uncommon, and I actually, more often than not, enjoy playing in the wind because it makes you not worry about score so much. You worry about hitting the shots one shot at a time, and you play a little smarter."
McNeill had a 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 a 67.
"Short game today was very good, and approach shots and putting," Ishikawa said. "Everything went well. That resulted in birdies and some nice par saves. So, the short game was the key thing."
He also played in the calmer morning conditions.
"I was lucky, but as I progressed toward the end, the wind got stronger and the conditions got tougher," Ishikawa said. "But under the strong wind conditions, I understood the difficulty of the course better. So I appreciate the design of the course more now."
Todd Hamilton shot a 69 to join Ishikawa at 7 under.
"I'm pleased with the way I've played," Hamilton said. "I haven't played very well for a long, long time, and it's nice to see not just a good nine holes, but a good 18 that I had yesterday and then another good 18 the following day."
Michael Bradley, the winner in 2009 and 2011, was 1 under after a 71.