With the game tied 92-92, Finley collected a pass from a driving Tony Parker and fired the 3-pointer with 1.3 seconds left to play. The shot clock had already run down but game officials ruled the shot was not reviewable.
Andres Nocioni missed a 3-point attempt for the Kings as time expired.
Parker led all scorers with 25 points and Roger Mason had 22 for the Spurs, who have won two straight and ended the day tied with Houston for first-place in the Southwest Division. The Spurs, Rockets and Portland Trail Blazers share the third spot in the Western Conference playoff chase at 52-28.
Spencer Hawes led Sacramento with 24 points. Nocioni had 11 points and eight rebounds for the Kings, who have lost eight straight games.