The Kings ended their longest losing streak of the season at six games and won on the road for just the fourth time this season. Sacramento finished a six-game journey at 1-5 and will play 11 of its next 14 contests at home.
Washington had a nine-point lead in the third period but fell behind for good with 4:57 remaining in the game.
The Wizards trailed by only three when Thornton began a 6-0 run with his tip-in. Isaiah Thomas then made a layup and Chuck Hayes hit two foul shots to put Sacramento ahead 112-103 advantage with 1:49 to go.
Thornton and Tyreke Evans both had 22 points for the Kings. Thomas added 16 points and 16 rebounds.
Washington, which has lost four straight, got 32 points from Jordan Crawford.