Neal sank five treys in all, including the game-tying shot with 5.7 seconds left in the fourth quarter and the go-ahead basket late in the extra frame.
He finished with 17 points while Tony Parker pumped in 30 with 10 assists as the Spurs reeled off their 10th straight victory.
The Clippers were led by Blake Griffin, who notched the first 20-20 game of his career with 22 points and 20 rebounds.
2014: NFL Cheerleaders [PHOTOS]
Michael Sam cut from the Dallas Cowboys