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.