The victory was the first for Rutgers coach Mike Rice since returning from a three-game school-imposed suspension for inappropriate behavior earlier this week.
The Scarlet Knights (10-3, 1-1 Big East) led by 14 points at halftime only to see the Panthers (12-3, 0-2) twice close the gap to two points in the final 5 minutes, the last time at 55-53 on a dunk by Steven Adams with 3:24 to play.
Carter, who came off the bench for only the fourth time this season, hit a 10-footer in the lane with 2:53 to go and Dane Miller added two free throws after James Robinson and Tray Woodall missed 3-pointers on the ensuing possession to secure the game.
Myles Mack added 11 points and Miller finished with nine points and six rebounds for the Scarlet Knights, who were coming off a 78-53 loss to No. 7 Syracuse in Rice's return.
J.J. Moore came off the bench and had a team-high 14 points for Pittsburgh, which was beaten 70-61 by No. 14 Cincinnati on Monday. Woodall added 11 points, but only shot 3 of 11 from the field in a game the Panthers were limited to 37.5 percent shooting.
Pittsburgh's inability to hit from the outside caused it to trail 39-25 at halftime and only when they managed to push the ball inside and play much better defense did it get back into the game.
The Panthers limited Rutgers to six points in the opening 12 minutes of the second half to get back in the game, but they never could get over the hump.
Even when they were lucky, it didn't help. Durand Johnson banked in a 3-pointer as the shot clock expired to get Pittsburgh within 53-51 with 4:23 to go but the Panthers failed to come up with an offensive rebound on a missed jumper from the corner by Mike Poole. Miller got the board and fed Jerome Seagears for a layup, which was credited when goaltending was called.
After a turnover by Woodall and a missed shot by Miller, Woodall fed Adams for a dunk, cutting the lead to 55-53.
Carter hit a short jumper in the lane and the Scarlet Knights were never threatened.
Pittsburgh lost forward Talib Zanna late in the game when he picked up his fourth foul on a play that was ruled a flagrant foul. Carter got his final two points making the free throws on the technical.
Rutgers hit its first six shots and 9 of 12 in racing to a 22-8 lead in the opening 8 minutes.
The Panthers made a brief 10-2 run to draw within 24-18 in the next 4 minutes but the Scarlet Knights got seven points from Carter in a 10-1 spurt.
Rutgers shot nearly 58 percent from the field (15 of 26), making 6 of 10 from long range.
Pittsburgh, which settled for jumpers most of the opening 20 minutes, shot 32 percent, making only 4 of 14 from 3-point range.