Since taking over from Don Nelson last weekend, Johnson is 3-0.
The Mavericks won their fourth overall and climbed to within 4 1/2 games of slumping San Antonio for the division lead.
Keith Van Horn contributed 24 points in his best game since being traded to the Mavericks. Baron Davis led the Warriors with 22. They had won seven of their previous 11.
Dallas had a three-point lead at halftime and then limited the Warriors to 16 points in the third period.