Brandon Hatton scored 10 and the Catamounts (5-4) forced 20 turnovers and converted 32 Wagner personal fouls into 25 of 39 free throws.
Marcus Burton scored 22 for Wagner (2-6), which won the rebound battle 40-38 but shot just 26.9 percent from the field to 34.9 percent for Vermont.
There were seven first-half lead changes and three ties until Wills hit a 3-pointer at 6:05 to put Vermont in front 14-13. Bell-Haynes hit four free throws and Kurt Steidl had two to end the half and the Catamounts led 27-25 despite being outshot 32 percent to 22.2 percent.
Vermont opened the second half with a 10-2 run, but Wagner stayed close, using a 9-1 run and five free throws by Burton to pull within three, 43-40. Vermont replied with a 9-1 run to stay ahead.