The Warriors, who let an 18-point lead get away in the fourth quarter of the series opener in a game they evenly lost in double overtime, held off another San Antonio comeback bid to steal home-court advantage in the Western Conference semifinals.
With the series tied at 1-1, Golden State will host the next two contests on Friday and Sunday.
Thompson hit 8-of-9 from 3-point range and scored 34 points overall. He also grabbed 14 rebounds and helped push the Warriors to a 20-point lead in the third period.
San Antonio came as close as six points on a 3-pointer by Manu Ginobili with 4:23 to play, but the Spurs then went scoreless for 4 minutes to miss out on a chance for another huge rally.
Stephen Curry added 22 points for the Warriors, the No. 6 seed in the Western Conference who knocked off Denver in six games during the opening round of the playoffs.
Beautician charged with giving client fatal silicone butt injection
Astronomers offer more expansive view of universe