Jordan Burgess had 12 points for VCU (4-2).
Old Dominion (3-3) made six of its first seven field goals to take a 16-8 lead five minutes in, but VCU responded with a 10-0 run before the teams with into halftime tied at 35-all.
Johnson hit back-to-back 3-pointer to spark an 11-3 spurt that put the Rams up 11 midway through the second half, but a 3 by Zoran Talley trimmed Old Dominion's deficit to 58-55 with five minutes to go.
Korey Billbury and Lewis hit 3s on consecutive VCU possessions as the Rams scored 10 of the 11 points and pushed their lead back into double digits, 68-56, with 1:13 left.
Aaron Bacote scored 21 and Trey Freeman added 17 for Old Dominion.
The teams combined to make 21 3-pointers.