Mario Moody finished with 12 points and nine rebounds, and Kenneth Ortiz and Jonathon Williams added 10 points apiece for Wagner (7-5).
Trailing by 15, 49-34, with 9:28 remaining in the second half, Monmouth (5-9) cut the lead to just one, 55-54, behind Andrew Nicholas’ three-point play with 1:34 left to play.
After Moody made a pair of free throws to extend Wagner’s lead to three, 57-54, Jesse Steele’s layup made it 57-56 with 47 seconds remaining.
Burton connected on 3 of 4 free throws in the last 25 seconds and Dion Nesmith had a crucial turnover for Monmouth with 9 seconds left as Wagner held on for the victory.
Nicholas led the Hawks with a game-high 21 points.