Myles Mack had 15 points and four assists and Wally Judge added 12 points, six rebounds and three assists for Rutgers (8-2), which is 2-0 under associate head coach David Cox.
Cox is filling in for coach Mike Rice, who is suspended without pay for three games due to violation of athletic department policy.
Howard (3-10) got 16 points from Anton Dickerson and 10 points and six rebounds from Mike Phillips.
Leading 43-32, Rutgers broke it open when Carter scored five points in an 8-0 run. The Scarlet Knights extended their lead to 23 twice and opened their largest advantage on the game’s final basket, a 3-pointer by Mike Poole.
Rutgers shot 60 percent (33 of 55) for the second straight game and forced 18 turnovers that resulted in 28 points.
After Theodore Boyomo’s layup gave the Bison a 22-21 lead, the seventh lead change of the first half, Carter hit a 3-pointer to start a 16-6 run that gave Rutgers a 37-28 halftime advantage.
Carter scored all seven of his first-half points during the run, while Howard committed five turnovers in a span of seven.
After taking a 60-37 second-half advantage, Rutgers allowed the Bison to get within 15 twice but, with the score 64-49, Carter converted a four-point play and Judge, who shot 6 for 6, got a slam to seal it with under 4 minutes left.
The Knights finished 8 for 12 from 3-point range with Mack going 3 for 4 and Carter 3 for 5. Rutgers finished with 13 steals, including three by Carter.
It was the first meeting between the schools, and the victory extended Rutgers’ record to 11-0 against Mid-Eastern Athletic Conference members.