Neller, 6 for 13 from beyond the arc, got help from Chase Plummer, who scored 17 points on 8-of-12 shooting.
The Retrievers (5-16, 3-5) led by 27-26 at halftime. But they held on as the Bearcats (3-18, 1-7) lost for the 14th time in their last 15 games.
Jordan Reed scored a game-high 21 points for Binghamton, but that wasn’t quite enough. Not even with Jimmy Gray’s 11 points.
Ryan Cook’s second trey with 3:06 remaining gave UMBC the lead for good, 55-53, with 3:06 remaining. Binghamton’s Roland Brown missed the second of two free throws to cut the lead to one. UMBC held on.
The Retrievers were a decisive 10 for 24 on treys. Binghamton went 4 for 20, with three by Gray.