Marshall led 51-35 with less than 15 minutes left before Tennessee began its comeback.
The Volunteers' 26-2 run included one stretch in which they scored 19 straight points.
Although Marshall was coming off an 11-21 season and had lost an exhibition game 101-89 to Division II school Newberry on Sunday, the Thundering Herd gave Tennessee all it could handle.
After leading 38-35 at halftime, Marshall opened the second half on a 13-0 run and owned a 51-35 lead after Kelly's basket with 14:59 remaining.
That 16-point lead vanished in less than four minutes.
The Volunteers' 26-2 run included one stretch in which they scored 19 straight points.
Although Marshall was coming off an 11-21 season and had lost an exhibition game 101-89 to Division II school Newberry on Sunday, the Thundering Herd gave Tennessee all it could handle.
After leading 38-35 at halftime, Marshall opened the second half on a 13-0 run and owned a 51-35 lead after Kelly's basket with 14:59 remaining.
That 16-point lead vanished in less than four minutes.