Shenandoah (5-3, 4-2 USA South) ensures itself of its best season since 2004 with the victory over AU (3-6, 2-4).
With one game left, SU will finish at least the .500 mark for the first time since the 2004 USA South co-champion squad went 7-4.
The Hornets led just 10-3 at the break but scored four touchdowns in the third to seal their eighth victory in 12 lifetime meetings with Averett.
The defense was the story of the day as SU picked off AU quarterbacks four times, returning two of them for touchdowns, and set up the offense with a short field on two additional occasions.
Shenandoah used a muffed Averett punt to key its first scoring drive. Gunner Philip Volz recovered the Anthony Terry fumble at the Cougars 23, and six plays later Daniel Wright found Rico Wallace on a fade pass for the 1-yard score.
Another special teams mistake, this one an unsuccessful fake punt, led to a nine-play, 27-yard SU drive that ended with a 22-yard Andrew Lloyd field goal.
Early in the third, a forced fumble led directly to what proved to be the game-breaking score.
Ke'Von White fumbled on his own 10, and thanks to a Donny Dotson recovery at the 9, SU had prime position for its second drive of the half.
It took just one play to cash in, as Brad Martz busted through the middle for his fourth rushing TD of the season and the Hornets led 17-3 with just over 11 minutes remaining in the third.
Two plays later Byron Mitchell gave SU another short field with his fourth interception and the offense over on the AU 5. Wright found Martz on a 4-yard TD pass and the Hornets had all of the points they would need to seal the win.
The offense was outgained 420-277, including 224-78 through the air. Carl Joseph accounted for nearly half of the Hornets 197 rushing yards with his school-record 88-yard TD with 6:47 to play in the third.
Gibbs paced the defense with 11 tackles (seven solo) and had the 84-yard 'pick six'.
Shenandoah completes its season, and its run in the USA South, next Saturday with a 1:00 contest at N.C. Wesleyan.