De’Mon Brooks scored 22 points for the Wildcats (1-1), who led 50-36 early in the second half.
The Lobos (1-0) got back into the game in part because of a dominating performance on the boards in the second half. After getting outrebounded in the first half, New Mexico held a 27-7 margin after the break.
The Lobos also were strong from the line, outscoring the Wildcats 38-15.
Davidson ran out to a 10-0 start and stretched its advantage to its largest, 27-11, midway through the first half.
The Wildcats had five players in double figures, while Jake Cohen grabbed eight rebounds.
New Mexico got 17 points from Kendall Williams and 14 from Alex Kirk, who also led the Lobos with seven rebounds.