The Phoenix (7-1, 5-0 Southern Conference), who scored 39 unanswered points after falling behind 7-3 early in the second quarter, won their seventh consecutive game, the program's longest win streak since 1981, when Elon was in the NAIA.
The loss was the sixth in a row for Chattanooga (1-7, 0-4), which had 87 yards of offense after the first quarter but finished with 125. The Mocs' lone touchdown came on a 5-yard pass from Jare Gault to Clint Woods on the first play of the second quarter.
Elon's first six points came on field goals by Andrew Wilcox, who set a school record for field goals in a season with 16.
Brandon Newsome, who rushed for 95 yards on 23 carries, then scored on a 2-yard run with 5:49 to play in the first half to give the Phoenix a 13-7 lead.
Shuman, who had just 84 rushing yards entering the game, got 54 on his first carry in the second quarter.
He scored Elon's final touchdown on a 19-yard run with 43 seconds left in the game.