Kress finished with 122 yards receiving and Ahmari Davis added a career-high 133 rushing yards and two TDs for New Mexico (2-1).
New Mexico started the game well when Jerrick Reed II picked off Adkins' first pass, taking it 43 yards for a touchdown.
The game was tied 31-31 at halftime before Adkins connected with Tony Nicholson for a 3-yard touchdown to put New Mexico State (0-4) up 38-34.
But Kress got loose for his second score on a 20-yarder, and on the next possession, Tuioti found Cedric Patterson III for a 62-yard scoring strike and a 48-38 advantage for the Lobos entering the fourth quarter.
The game was tied five times in the first half before New Mexico pulled away in the third quarter.
The Lobos led 55-38 five minutes into the fourth quarter until New Mexico State rallied for two late touchdowns.
The win keeps the Lobos on track to meet their goal of six wins. With winnable games on tap the next two weeks against Liberty and San Jose State, New Mexico would be in good position to achieve bowl eligibility.
After games against nationally ranked Washington State, Alabama and rising San Diego State, the Aggies desperately needed the victory over their rivals. Dating back to last season, New Mexico State has gone 1-9 in its last 10 games.
New Mexico: The Lobos visit Liberty on Saturday. The Flames won a wild shootout in Albuquerque last year 52-43 for their first FBS road victory.
New Mexico State: The Aggies are home Saturday against the Mountain West's Fresno State. The former Western Athletic Conference opponents have not met since 2011 when the Bulldogs won 48-45 in Las Cruces.
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