McNeill, at 13-under 203, is trying to win for the first time since the Frys.com Open in 2007 when he was a PGA Tour rookie. He eagled the par-5 fifth, dropped strokes with three-putt bogeys on No. 7 and 8, then birdied five of the last 10 holes on the Trump International layout.
The former Florida State player has a conservative approach on the wind-swept course.
"First of all, patience," McNeill said. "This morning the wind didn't blow at all. The wind picked up this afternoon, so you got to stay patient when it's windy. You got to hit some different shots. And sometimes you just take what it gives you. Just patience is what I'll be trying to do.
"I don't foresee trying to do anything different. Obviously, I'm not going to try and force anything unless I have to coming down the last few holes."
He finished fifth last year.
"Last year was my first year here, and I played well," McNeill said. "It looks a lot like the golf courses back in Florida where I'm from. I'm playing on Bermuda grass and Bermuda rough, and saltwater ponds. We have a lot of that at home. So I don't feel uncomfortable at all. When I go out on the West Coast, it's very uncomfortable because it's just foreign to me. So I get out here and I'm very comfortable."
Stenson had a 65, and Stadler shot a 66.
"If I can stay patient, as I've done these first couple of days, and chip and putt well, I hope I get a chance tomorrow," Stenson said.
Stadler birdied four of the first five holes in his bogey-free round.
"I putted very well," Stadler said. "It was great today. For the most part this year, I've putted a lot better than I have in the past four or five, six years. I felt really comfortable on these greens.
"I've played well here in the past where I've hit the ball just phenomenally well every day and struggled with the putter, and it's funny to be up near the top this week with the complete opposite."
Second-round leader Matt Jones was two strokes back at 11 under after a 72.
Ryo Ishikawa, in Puerto Rico because he failed to qualify for the World Golf Championship this week at Doral, shot a 69 and will go into the final round just three shots out of the lead. Ishikawa has never finished higher than a tie for fourth on the PGA Tour. He is trying to become the fifth straight player in his 20s to win on the PGA Tour.
Michael Bradley, the winner in 2009 and 2011, was 1 under after a 72.