Arizona and New Mexico have a storied football history, but it's less of a rivalry and the Wildcats have instead become regular boogeymen for the Lobos. Prior to the two founding the Border Conference in 1931, Arizona had built up a 14-3-1 record over New Mexico including a 33-0 shellacking in 1930.
New Mexico and Arizona started playing for the Kit Carson Rifle in 1938, which New Mexico held for its first three seasons until Arizona first took possession in the 1941 season. Arizona retained the rifle for 15 years until New Mexico finally found a stretch of wins from 1957-65. The two teams played every year until the 1978 season when Arizona joined the Pac-12 after building up a 40-18-3 record over the Lobos.
The Kit Carson Rifle was retired ahead of the 1997 Insight.com Bowl when the two teams were set to face off at Arizona Stadium. Arizona won that matchup, lost both games in a home-and-home series in 2007 and 2008, and then won the 2015 New Mexico Bowl against the Lobos on their home turf. The return of this game this season is nice for tradition's sake, but Arizona has simply evolved into the greater athletic power over the years.