The Mavericks trailed most of the night before Carter's 3-pointer put them up for good, 84-81, with 8:51 to play. The basket was part of a 12-4 run that gave Dallas a 92-85 lead on Jae Crowder's 3 with 6½ minutes to go.
Phoenix never got closer than five again.
The fourth quarter collapse was in contrast to the Suns' emotional, come-from-behind victory over the Los Angeles Lakers two nights earlier.
"Our intensity was not the same like last game," Dragic said. "We were not engaged in defense."
Dallas' only lead of the first half was at 2-0 but the Suns never were up by more than seven in the first two quarters and it was tied at 54 at the break.
Dragic had 10 points, four rebounds and four assists in the first quarter, with the Suns holding a 31-29 lead. Brown opened the second quarter with a pair of 21-footers to make it 35-29, then capped an 11-4 run with a 3-pointer to put Phoenix up 40-33 with 9:10 left in the half.
The Mavericks caught the Suns with a 15-8 surge, tying it at 50 on Mayo's 3-pointer 2:16 before the break.
The Mavs went nearly 4½ minutes without a point as the Suns scored 11 straight to go up 71-61 on Marcin Gortat's layup with an assist from Dragic with 4:45 left in the third quarter. But Dallas responded with a 13-2 run to take the lead for just the third time of the night, 74-73, on Brandan Wright's inside basket with 1:12 left in the period. Brown's basket 20 seconds later put Phoenix up 75-74 entering the fourth.
NOTES: The Suns play seven of their next eight on the road, where they are 4-19, second-worst in the NBA (Washington is 3-20). ... For the second time in three games, Hunter used rookie Kendall Marshall as the backup point guard instead of Sebastian Telfair. ... Dallas is 13-16 without Nowitzki, 7-11 with him. ... The teams don't meet again until April 10 in Dallas, where the Mavs can sweep the season series. ... Dragic has one career triple-double. ... The Suns are 3-3 since Hunter took over.