The Spurs kept alive their hopes of claiming the No. 1 seed in the playoffs while Phoenix guard Steve Nash played what was perhaps his last game as a member of the Suns.
San Antonio kept pace with Chicago at the top of the NBA standings after the Bulls defeated Indiana earlier in the evening. The Spurs and the Bulls have 49-16 records going into Thursday's regular-season finale.
To finish as the No. 1 seed and have home-court advantage throughout the playoffs, the Spurs must defeat Golden State while Chicago loses against Cleveland.
The Suns closed out their regular campaign outside the playoffs and Nash, who has the fifth most assists in NBA history, is headed for free agency.
Phoenix had a chance to pull out a win against the Spurs, but Sebastian Telfair missed a 3-point try with 21 seconds to play and his team trailing by two.
Mills scored 27 points to lead San Antonio and Tiago Splitter had 26. Spurs Coach Gregg Popovich showed what little regard he had for the possibility of his team being the No. 1 seed when he rested Tim Duncan, Tony Parker and Manu Ginobili for the entire game.
Shannon Brown scored 21 points to pace the Suns.