Rodriguez hit a 3-pointer with 16:53 to go for a 38-37 lead and Binghamton led the rest of the way.
Everson Davis made a layup at 1:38 for a 71-68 advantage, and Binghamton did the remainder of its scoring from the free-throw line, making 10 of 12 in the final minute, including five from Marlin Beck II and four from Rodriguez.
Beck finished with 17 points for the Bearcats, who were 28 of 53 from the field for 52.4 percent, including 10 of 18 from 3-point range.
Brandon Peel had 12 points and 13 rebounds, with Khalen Cumberlander scoring 18 points and Austin Nehls 17 for the Blue Devils.
The victory was the first for the Bearcats (1-3) in five games with CCSU (0-4).