Brown scored 24 points off the bench while Marcin Gortat produced 23 and Michael Beasley 21. Beasley added 15 rebounds and Gortat pulled down 10.
The Suns had lost their previous two outings and won on the road for the first time this year.
Phoenix opened a 16-point lead during the latter half of the third quarter, but the Bobcats rallied to tie it early in the fourth. The Suns then pulled away with Gortat's two free throws giving Phoenix an eight-point cushion in the final minute.
Byron Mullens paced the Bobcats with 24 points.
The teams combined to attempt 50 3-point shots with Phoenix going 12-of-28. The Suns shot 46 percent from the field overall and outrebounded Charlotte 49-39.
It was just the third game of the season for the Bobcats and they have lost two of them.