Nick Johnson led the Wildcats (6-0) with 23 points and Kevin Parrom chalked up 14 points and eight rebounds.
Arizona trailed 35-27 at halftime but held the Eagles (6-2) to 20 points in the second half and took the lead 45-44 on Johnson's layup with 13:08 to play.
Southern Miss came back to grab a 51-49 lead with 5:53 to play but Johnson assisted on a 3-pointer by Parrom with 4:50 to play that gave Arizona the lead for good.
Neil Watson led Southern Miss with 17 points and Michael Craig added 10 points. The Eagles lost their second consecutive game.
Celebrity Families of 2014 [PHOTOS]