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.
Miami has lost running back Gus Edwards for the entire season because of a left foot injury.
Virginia Tech will wear a decal on its helmets against No. 1 Ohio State on Monday night to honor slain Roanoke television journalists Alison Parker and Adam Ward.
South Carolina football players will wear stickers on their helmets this season to honor the nine people who died in a shooting at Emanuel AME Church in Charleston this past June.
Washington has found its starting quarterback, but coach Chris Petersen said the Huskies will keep that information under wraps until Friday's season opener at No. 23 Boise State.
Joey Counts scored on a 1-yard run on fourth-and-goal with 2 seconds left to give Montana a 38-35 victory over four-time defending FCS champion North Dakota State on Saturday.
Transfer Vernon Adams will be the starting quarterback when Oregon begins its season against Eastern Washington on Sept. 5.