Green's 17-yard run in the third quarter gave the Mocs (2-1) the lead. After recovering an Eastern Kentucky fumble, Chattanooga marched 48 yards to Tyson's 1-yard touchdown with 54 seconds remaining.
T.J. Pryor was 15 of 28 for 164 yards and two touchdowns passing for Eastern Kentucky (1-2).
Green rushed for 68 yards on 21 carries.
B.J. Coleman completed 26 of 40 passes for 277 yards with a touchdown and an interception for the Mocs, who shut out their opponent after halftime for the second straight game.
The Colonels were limited to 84 yards of offense in the second half.