Mo Alie-Cox had 19 points, JeQuan Lewis grabbed 10 rebounds and the Rams (8-5) scored 17 points off 10 North Florida turnovers.
North Florida entered the game leading the NCAA with 12.9 3-pointers per game, but was held to 7 of 19 by the Rams' defense.
VCU led 39-31 at halftime and pulled away on a 14-4 run in which Johnson scored two 3-pointers to lead 59-41 with 11:46 to play.
North Florida gained on a 9-2 run to pull within 73-64 with 3:35 left, but Billbury made back-to-back layups and VCU outscored the Ospreys 6-2 in the final 2:31.
Dallas Moore scored 24 points on 11-of-17 shooting, Chris Davenport added 13 and Demarcus Daniels 12 for North Florida (10-6).