For the first time in a decade, the Wildcats played a game as the top-ranked team in the country and backed up that lofty position by dominating the second half.
Ashley finished with 15 points, making 5-of-7 from the field overall as part of Arizona State's 51 percent shooting performance.
Kaleb Tarczewski added 14 points and Aaron Gordon had 11.
Arizona State, at 10-0, is one of 14 unbeaten teams remaining in major college basketball. No. 2 Ohio State and No. 6 Wisconsin also stayed perfect with wins on Wednesday.
Daniel Mullings scored 18 points and was the only player for New Mexico State (7-5) in double figures.