Cabrera, the Argentine whose only other PGA Tour victories came in the 2007 U.S. Open and 2009 Masters, built a three-shot lead before making things interesting with a pair of late bogeys. He finished at 16-under 264.
McNeill shot a season-best 61 for his fourth top-10 of the season and first since mid-March.
Webb Simpson had a 63 to finish third at 10 under.
Third-round leader Billy Hurley III bogeyed four of the first six holes to fall out of contention. He shot a 73 and finished in a seven-way tie for fourth at 9 under.