Smith was 6 of 7 in 23 minutes, as the Highlanders (6-23) snapped a two-game skid.
Javonte Green added 13 points and 10 rebounds and R.J. Price had 11 points and four steals for Radford.
The Highlanders forced 18 turnovers, leading to 24 points.
Tied early, the Highlanders scored seven straight to lead the rest of the way. Smith capped the run with a layup to make it 9-2 with 13:08 left in the first half.
After Radford stretched its lead to as many as 16, at 56-40 with 11:16 remaining, Binghamton responded with a 19-6 streak to cut the deficit to three with 17 seconds left. However, Binghamton wasn’t able to get any closer.
Ben Dickinson scored 14 points for the Bearcats (0-26).