Matt Bingaya added 15 for the Golden Eagles (5-3), who trailed for much of the first half.
Wesley Pietri scored 15 for the Badgers (1-7), who committed 21 fouls which the Golden Eagles converted to 17 of 26 free throws.
Pietri hit back-to-back 3-pointers and the Badgers led 24-16, but Southern Miss ripped a 13-2 run in which Suarez sank three treys. Hayes made a free throw with 2 seconds to play and the Golden Eagles took a 29-28 halftime lead.
Spring Hill rallied to a 45-42 second-half lead after a 3 by James Clarke, but Southern Miss retook the lead 48-47 on a dunk by Norville Carey. Sam Hutcheson pulled the Badgers to within two, 57-55, with a jumper, but Southern Miss sealed the win with nine free throws in the final 1:16.