Christian Wood's basket cut UNLV's deficit to 69-67 with 1:42 left and his dunk a minute later tied it at 69. After Goodman's basket, UNLV had its layup attempt stripped at the buzzer.
Hugh Greenwood had 22 points and eight rebounds for New Mexico (13-6, 5-2 Mountain West). The Lobos have held their opponents under 70 points in every game this season.
Greenwood's sixth and final 3-pointer gave New Mexico a 63-60 lead.
Wood scored 20 points for UNLV (10-9, 1-5), and Rashad Vaughn and Patrick McCaw added 13 apiece.
UNLV went on a 7-0 run, capped by Vaughn's 3-pointer, to take a 50-48 lead. New Mexico quickly tied it up, and Arthur Edwards steal and dunk gave New Mexico a 52-50 lead.