McNeill, who shared the second-round lead, finished 54 holes at 18-under-par 197 at the TPC at Summerlin.
Overnight co-leader D.J. Trahan only managed an even-par 72 on Saturday. He is tied for second place with Robert Garrigus, who carded a 4-under 68, at 13-under 202.
McNeill tripped to a bogey at the second hole, but recovered with a birdie at the par-5 third. He dropped another shot at the par-3 fifth, but that would be one of his last mistakes.
At the seventh, McNeill rolled in a 12-foot birdie putt, which kept him tied with Garrett Willis, an overnight co-leader who ran home a 15-foot birdie putt of his own at the hole.
The pivotal hole for McNeill was the par-5 ninth. Willis could not make birdie, but McNeill rolled in a 3-foot birdie putt to reach 14 under par and move one clear.
At the 11th, McNeill sank an 8-foot birdie putt and Willis made bogey. That gave McNeill a three-stroke cushion, which was the closest it would be the rest of the way.
He birdied the par-5 13th, then found some trouble at the short, par-4 15th. McNeill's drive left him in the left rough with a huge bunker in front of him. He pitched into that bunker and the ball plugged. McNeill blasted out to 3 feet to avoid a bogey.
McNeill reached the green in two at the par-5 16th. He had 42 feet for eagle, but did not hit a great putt. McNeill left himself with 6 feet for birdie, but the reliable putter converted the putt to move to minus-17.
McNeill drove into the right rough at the 18th, but it hardly mattered. He played his approach to 3 feet and holed the birdie putt to move five clear in search of his first PGA TOUR victory.
For McNeill it came down to putting.
'It's always big no matter what,' said McNeill. 'If you start hitting it better and making a few putts, your score can add up to a pretty good one. Hopefully it will continue.'
The fact that McNeill, a former assistant pro, has not won on TOUR is a tad misleading. He won last year's Q-school to get his card and at 122nd on the money list, he could use a big week just to secure his playing privileges for next year.
'It's just like any golfer's dream, you always want to win PGA TOUR events,' said McNeill. 'The first step is to get this one under my belt. I feel like I belong.'
Willis (73), Kent Jones (68), Bo Van Pelt (68) and John Huston (72) are knotted in fourth place at minus-12.
Cameron Beckman (68), Stephen Leaney (69), Jeff Gove (70), Bob May (71), Mathias Gronberg (71), Mark Wilson (71) and Jason Gore (73) are tied for eighth at 11-under 204.