Minnesota endured a disappointing campaign that included 31 victories.
Williams had 21 points, Chase Budinger had 15 and both Ricky Rubio and Greg Stiemsma had 12.
The Spurs finished second in the West behind defending conference champion Oklahoma City, losing at home for just the sixth time this season.
Tim Duncan had 17 points and 14 rebounds to pace the Spurs, who went 22-of-22 from the foul line.
Celebrity Breakups and divorces of 2014 [PHOTOS]