The Golden Eagles (6-5, 5-3 Ohio Valley Conference) ended a two-game losing skid and finished second in the league by rushing for 288 yards, their highest total of the season. Their previous best was 248 in the season opener against Pikeville.
Dontey Gay had his second 100-yard rushing game of the season with 102 yards on 10 carries.
Barnes, who alternated at quarterback with Sweeney, broke open a 14-7 game with touchdowns of 1 and 3 yards to give the Golden Eagles a 28-7 lead with 10:50 left in the third quarter.
The second and third strings played much of this fourth quarter for Tennessee Tech.
Charlie Jordan rushed for 90 yards and a touchdown on 19 carries for the Racers (3-8, 2-6).