The Mavericks battled from behind throughout the game and closed within a point with 43 seconds to play when O.J. Mayo made 1-of-2 free throws.
Dallas regained the ball and had a chance to take the lead when Brandan Wright headed for the basket for a layup attempt.
Bogut, however, blocked the shot to preserve the Golden State lead and Jarrett Jack made two free throws with 2 seconds left to finish the scoring. Golden State has won three in a row.
Klay Thompson hit 11-of-18 shots from the field and scored 27 points to lead the Warriors. David Lee added 15 points and pulled down 20 rebounds.
Mayo produced 25 points and the Mavericks also picked up 22 from Vince Carter.