The Wildcats (2-0), who play Notre Dame next Wednesday night in New York's Madison Square Garden, broke open the rough contest with runs of 17-5 and 14-0 in the second half.
Richard Jefferson scored five of his 11 points during the 17-5 surge as Arizona won its 34th in a row at home. The last two times the Wildcats played in the Preseason NIT, in 1990 and 1995, they won the championship.
Freshmen guards Jason Gardner and Gilbert Arenas scored 11 and 10 for Arizona. Loren Woods scored 10 of his 13 in the final eight minutes for the Wildcats.
Billy Keys scored 15 for New Mexico State. Mikko Noopila and Eric Channing each added 11.
The Aggies played Arizona for the first time since 1971 in a matchup that featured two of the game's most successful veteran coaches, the Wildcats' Lute Olson and the Aggies' Lou Henson.
Arizona led throughout, but the Aggies, with four starters back from last season, used a rugged defense to stay close into the second half. New Mexico State trailed 33-28 at the break.
Nooopila's 3-pointer cut the lead to 35-33 with 18:33 to play, then Arizona turned up the tempo.
Jefferson made two free throws and sank a 3-pointer and the Wildcats led 54-42. Freshman point guard Jason Gardner's steal and driving layup put Arizona ahead 48-36 with 12:36 to play. Gardner, who was fouled on the play, was called for a technical foul for taunting, his fourth personal.
Luke Walton capped the 17-5 run with two free throws to give Arizona a 52-38 lead with 8:24 remaining.
The Aggies managed one more rally. Keys scored five consecutive points, on a 3-pointer and two free throws, to cut it to 66-57 with 5:24 to go. But Woods scored four and blocked a shot during a 14-0 outburst that buried the Aggies.
The 6-foot-7, 238-pound Wright, last season's Pac-10 freshman of the year, scored 11 of the Wildcats' first 15 points.
With 2:37 to play, the Aggies were called for a technical for failing to substitute quickly enough after Noopila fouled out.