The Lobos (4-3, 1-1 Mountain West Conference) used three San Diego State miscues to account for 17 points, including Strother's 14-yard return of a blocked punt by Hank Baskett to give New Mexico a 14-0 lead in the second quarter.
San Diego State (3-5, 0-3 MWC) gained only 39 yards rushing and could not overcome four interceptions thrown by Adam Hall, including two at the New Mexico goal line.
Moore, who gained 89 yards on 15 carries, scored on runs of 2 and 3 yards. The latter touchdown put New Mexico ahead 24-7 early in the third quarter.
The Lobos also got three field goals - 48, 32 and 21 yards - from Wes Zunker.
Brandon Ratcliff returned Hall's first interception 14 yards to the San Diego State 19-yard line. That set-up Moore's 2-yard touchdown run in the first quarter, putting New Mexico in front 7-0.
Nick Speegle intercepted Hall in the third quarter and returned it 23 yards to the Aztecs' 20, which led to Zucker's 32-yard field goal.
Hall finished 25-of-48 for 291 yards.
Lynell Hamilton scored San Diego State's only touchdown on a 1-yard run in the second quarter that cut the Lobos' lead to 14-7.