Jeff Moturi completed 15 of 32 passes for 182 yards for the Miners (1-2), who won for the 50th time in the teams' 87 meetings.
Seth Smith rushed for 100 yards on 13 carries for the Aggies (1-2).
Heavy rain and lightning swept into the area 15 minutes after kickoff, forcing both teams to retreat to the locker room while most fans left Aggie Memorial Stadium.
Play eventually resumed just under three hours later with the Miners leading 7-0. UTEP stretched its lead to 31-0 before New Mexico State scored on a 1-yard run by Marquell Colston.
Veron Frazier added two rushing touchdowns for the Miners.