Cotton was the lone bright spot in a cold-shooting first half, sinking four 3-pointers to help the Phoenix take a 23-16 lead.
Green Bay dominated early in the second half with a 23-2 run. Rahmon Fletcher and Evans scored seven points apiece during the run to take a 46-22 lead.
Fletcher sparked the scoring flurry with a coast-to-coast layup, and Evans' steal and breakaway dunk and Cotton's fifth 3-pointer punctuated it.
Detroit committed eight turnovers in that 8-minute span.
The Phoenix (5-2, 2-0 Horizon League) have won five straight games for the first time since the 2004-05 season.
The Titans (2-5, 0-2), led by Thomas Kennedy's nine points, have lost 17 consecutive road games and 16 straight at conference opponents.