Curry, who was 16-of-26 from the field and 10-of-16 from beyond the arc, entered the fourth quarter with 41 points.
Charlie Villanueva's 3-pointer in the waning seconds of the third quarter got Dallas within 101-98 heading into the final frame, but Golden State began the fourth on an 11-3 run to create some distance.
Barbosa had six points during the surge. He coverted a layup and triple to start it and capped it by splitting a pair of free throws for a 112-101 Warriors margin with 7:43 remaining.
Chandler sandwiched baskets around a Parsons layup to whittle the gap to 112-107 midway through the period.
The Warriors, though, pulled away down the stretch, closing the game on a 10-1 burst.
Curry netted the final eight points, including a step-back left wing trey with just under a minute left.
Earlier, Parsons tallied nine points and J.J. Barea poured in seven as Dallas raced out to a 24-4 start before leading 42-25 following a quarter of play.
A 15-3 Warriors run in the second got the hosts back in it and they were within 62-58 going into the break.
Golden State has beaten the Mavericks five straight times ... Monta Ellis had 14 points against his former team for Dallas ... The Warriors shot 52.3 percent (45-of-86) from the field and connected on 19-of-38 from beyond the arc.