The fourth-ranked Jaguars trailed by four with 30 seconds left in regulation. Junior forward Fred Brathwaite knocked down four foul shots to send the game into overtime.
In the extra period, Augusta State out-scored West Georgia 16-7. The Jaguars improved to 5-2 in overtime games under fifth-year coach Dip Metress.
Augusta State (2-0) played in foul trouble the entire night, with guards Ben Madgen, Daniel Dixon and Caleb Brown all fouling out. Greg Hire also played just 24 minutes with four fouls.
Siler, a senior center, shot 9-for-12 from the field.
He also helped the Jaguars dominate the rebounding margin (46-28) and points in the paint (44-26).
Brathwaite tacked on 16 points on 4-for-16 shooting. He added nine rebounds and two steals in 38 minutes.
Madgen scored 14 points, while Dixon had 11 and Brown 10.
Augusta State shot 47 percent from the field, including a 7-for-19 performance from the perimeter. The Jaguars also shot 20-for-31 from the free-throw line.
West Georgia (2-6) shot 51 percent from the field, including 58 percent in the second half. The Wolves did themselves in at the free-throw line, shooting a woeful 15-for-33 (46 percent) from the stripe.
Augusta State returns to action Saturday when the face Paine College at 8 p.m. at Carter Gym.