UNC scored the first 12 points, led by 18 at halftime then ran off the first 11 after the break to blow the game open.
The Tar Heels spent much of the game shooting around 60 percent before finishing at 51 percent while doing a much better job of pushing the tempo than in Friday's season-opening win against North Carolina Central.
Freshman Marcquise Reed scored 18 of his 24 points in the first half for the Colonials (0-2), who hung around in the first half but had no way to slow the Tar Heels once they got rolling.
That was particularly true of Meeks and Johnson.
UNC coach Roy Williams has talked throughout the preseason about how someone needs to provide reliable inside scoring production to complement the team's deep perimeter. Johnson and Meeks entered the year as the most likely candidates, and Sunday offered a glimpse of their potential to grow into those roles.
Johnson had 15 by halftime and finished 10-for-15 from the field with eight rebounds.
Meeks had 15 points and seven rebounds by the midway point of the opening half and finished 6-for-7 from the field and 9-for-14 from the foul line with 12 rebounds.
Paige, a preseason All-American, also bounced back from a quiet opener with three 3-pointers, while freshman Justin Jackson added 13 points. Reed was the only player to find a rhythm for Robert Morris, who return three starters from a team that won last year's Northeast Conference regular-season championship. Preseason all-conference pick Lucky Jones was scoreless without a shot attempt in the opening half. He finished with six points on 2-for-7 shooting before fouling out with 5:50 left.
The game was part of the Battle 4 Atlantis, though tournament play doesn't begin until the night before Thanksgiving.
Robert Morris: The Colonials had never faced the Tar Heels before. ... This started a stretch of five games away from home. ... Robert Morris shot just 28 percent after halftime and 36 percent for the game.
North Carolina: J.P. Tokoto had a career-high seven assists by halftime and finished with 10, more than any UNC player had last year. ... UNC took a 49-31 rebounding advantage, scored 20 second-chance points and 24 points off turnovers. ... The Tar Heels hit 27 of 36 free throws (75 percent).