Old Dominion (18-6, 7-5 Conference USA) is 5-5 since being nationally ranked in early January.
Both teams started slowly, with ODU holding a 6-5 lead a little more than five minutes in. Julian Washhburn's 3-pointer put UTEP up 15-11 with nine minutes left in the half, and then the Miners outscored ODU 13-8 to lead 28-19 at the break. The Monarchs made just seven baskets before intermission.
A pair of Aaron Bacote free throws with 3:02 left cut the deficit to six. But with JMU forced to foul, UTEP responded by making 12 of 14 from the line in the last 2:42 to hold on going away.
Old Dominion shot 31 percent and just 3 of 16 beyond the arc.
UTEP (18-7, 10-3) moves one game behind conference leader Louisiana Tech.