The win keeps Marshall tied with Middle Tennessee in second place in the Conference USA standings, two games behind Alabama-Birmingham.
Kelly gave the Thundering Herd an 80-76 lead with just over two minutes left in regulation. Anton Waters and Aaron Cosby each scored to tie the game at 80-80 with 59 seconds, forcing overtime.
Kelly hit a 3-pointer, a jumper and dunked in under a minute to put Marshall ahead, 94-92 with 18 seconds remaining.
Kelly and Jon Elmore each scored 24 points and Elmore added 10 assists for Marshall (13-12, 9-3). Terrance Thompson grabbed 10 rebounds.
Fredrick Edmond scored 25 points and Justin Johnson added 19 points and 11 rebounds for the Hilltoppers (12-13, 4-8).
