Mike Dunleavy had 33 points, seven assists and six rebounds to lead the Pacers (29-43), who trail the Hawks by 2½ games after losing their second straight. Danny Granger added 19 points before fouling out in the wide-open game that featured 27 3-pointers.
The Nets blew a 16-point first-half lead and needed a 21-11 spurt to end the third quarter to take the lead for good after Indiana rallied to tie it at 77 on two free throws by Granger.
Carter, who was limited to six points in the first half, then took over. He hit a floater in the lane to ignite the run and later added a 3-pointer, two free throws and a jumper.
Bostjan Nachbar, who added 18 points off the bench, hit two more 3-pointers in the run that ended with Marcus Williams banking in a 3-pointer at the buzzer for a 98-88 lead.
Indiana, which stayed in it despite allowing the Nets to score a season-high 42 first-quarter points, got to within 113-109 when Granger converted a four-point play after nailing one of the Pacers' 14 3-pointers.
However, Carter nailed a 3-pointer, Harris added a jumper and Nachbar hit his fourth 3-pointer to give the Nets a 121-111 lead in the closing minutes.
Trailing 68-52 late in the first half, Indiana got back in it with a 14-point run that bridged the end of the first half and the start of the third quarter.