Carter hit 9-of-10 free throws and stole the ball twice for the Scarlet Knights (10-3, 1-1 Big East), who shot 51.9 percent from the field.
Myles Mack chalked up 11 points and Dane Miller added nine.
Pitt (12-3, 0-2) played its first true road game of the season and remained winless in the Big East.
J.J. Moore led the Panthers with 14 points and Tray Woodall scored 11.
Rutgers led 39-25 at halftime and needed as much cushion as it could get to hold off Pitt's 37-point performance in the second half. Durand Johnson's 3-pointer cut Rutgers' lead to 53-51 with 4:27 to play, but the Knights used repeated trips to the free throw line in the closing minutes to keep the Panthers at bay.