Edwards had seven receptions for 82 yards, including scoring passes of 28 and 9 yards that helped give the Miners a 24-17 lead at halftime. Josh Bell also scored for UTEP (2-6, 1-3 Conference USA) on a 14-yard run.
Lamaison was 11 of 16 for 157 yards before leaving in the second quarter with a hamstring injury.
Ryan Griffin completed 28 of 44 passes for 363 yards and two touchdowns for Tulane (1-6, 1-2). Justyn Shackleford had six catches for 130 yards, including a 31-yard touchdown; Ryan Grant added six receptions for 115 yards, including a 15-yard TD.
The Green Wave had 440 yards of offense, just 5 less than UTEP, but managed only a field goal on five second-half possessions.