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.