The Rams (15-5, 7-1 Colonial Athletic Association), who have won six consecutive games, are tied with Hofstra for first in the conference.
Old Dominion (14-5, 5-3) took a 46-45 lead on Chris Cooper's layup with 6:50 left to play, but Ed Nixon hit a layup and Burgess made a 3-pointer for a 50-46 advantage with 5:12 remaining. The Monarchs cut the deficit to 52-50 with 3:38 left, but Joey Rodriguez's 3-pointer pushed it to 55-50 with 1:56 to play.
Nixon added 13 points for the Rams.
Darius James and Ben Finney scored nine points each for Old Dominion, which shot 33.3 percent from the field (9 of 27) in the second half. Leading scorer Frank Hassell, who was averaging 13.1 points, was held to six.