The semifinal victory puts North Carolina (3-1) into Sunday's finals against second-ranked and defending national champion Louisville.
All six of Paige's field goals came from beyond the 3-point arc. He also sank eight free throws.
Brice Johnson converted eight free throws and finished with 24 points.
Cedrick Lindsa led Richmond (3-2) with 29 points. Kendall Anthony scored 13.
North Carolina led 36-33 at halftime and pulled away with an 8-0 run late in the second half.
Louisville beat Fairfield 71-57 in Saturday's second semifinal game.
Swim Week Miami Beach 2014 [PHOTOS]