Brandon Betancourt ran for a 5-yard touchdown to pull the Aggies within 29-21. Ellison answered with a quarterback draw from 32-yards out to stretch the Eagles' lead to 36-21 with 2:34 to play. Betancourt ran for a 3-yard touchdown with 20 seconds remaining to cap the scoring.
Ellison finished with 145 yards on 16 carries, including a 7-yard score in the first quarter.
Alfred Ramsby ran for a 7-yard touchdown to give Georgia Southern (4-2, 3-0 Sun Belt Conference) a 19-14 lead. Alex Hanks made a 30-yard field goal and Ean Days punched it in from the 1 to stretch the Eagles' lead to 29-14 late in the third quarter.
Tyler Rogers threw for 329 yards and three interceptions for New Mexico State (2-4, 1-1).