The victory improved the Colonials to 3-0 for only the second time in the program's 31-year history.
Tyrece Gibbs and Jermaine Anderson each had 13 points for the Wildcats (0-4), a member of the America East Conference that was playing the second of three consecutive games against Northeast Conference foes.
Derek Coleman added 12 points and nine assists for the Colonials.
New Hampshire led 36-34 at halftime, but Robert Morris began the second half on a 13-0 run and never led by less than eight the rest of the contest. The Colonials shot 64 percent in the second half and 53 percent for the game. New Hampshire shot 55 percent in the first half but only 32 percent in the second.
Robert Morris started 3-0 during the 1989-90 season, a campaign in which the Colonials won the Northeast Conference championship and played in the NCAA tournament. The Colonials have never started 4-0.