Gary Neal missed a 3-point attempt for the Spurs just before the buzzer, leaving San Antonio with a second straight loss heading into the playoffs.
The Spurs finished one game behind Chicago for the best record in the NBA, but will be the top seed in the Western Conference. Both San Antonio and Chicago lost just five home games this season.
Marcin Gortat led Phoenix with 21 points and 17 rebounds. The Suns closed a disappointing season with a 40-42 record and wound up six games out of the playoffs.
Phoenix led by as many as 18 points in the first half.