Georgia Southern (9-9, 2-1 Southern Conference) shot 50 percent overall, including 11 of 21 from beyond the arc. Jelani Hewitt added 21 points as well, and Matias pulled down 10 rebounds.
Furman (6-12, 0-5) was led by Stephen Croome with 26 points.
Furman led the entire first half and was up by as much as 10 before the intermission, but Georgia Southern trimmed the lead to 3 at the half as Bussey drilled a 3-pointer with 8 seconds remaining.
The Eagles trailed by four late in the second half, but Matias hit one of two from the line, then Hewitt drained a trey with 21 seconds left to force overtime.
Georgia Southern scored first in overtime and never relinquished the lead.