Jack made a 14-foot jumper starting the extra frame and the Warriors never looked back, outscoring the Spurs 13-3 down the stretch to bounce back from a 102-92 loss in Game 3.
Jack also grabbed seven rebounds while Harrison Barnes scored 26 points and hauled down 10 rebounds for Golden State, which dominated the boards 65-51 thanks to Andrew Bogut's 18 rebounds.
Stephen Curry put in five 3-pointers en route to 22 points for the winners.
The Warriors will attempt to grab a series lead on the road in Tuesday's Game 5.
Many Ginobili netted 21 points while Tim Duncan provided 19 points and 15 rebounds for San Antonio, which was held to 35.5 percent shooting from the field.