Theodhosi, with 21 carries, had his second 100-yard game this season after missing the 2010 and 2011 campaigns with knee injuries.
Donnelly hit Andrew Marks with a 7-yard pass with 4:02 elapsed to open the scoring. After the Hoyas tied it at 10 with 11:22 left in the first half, Theodhosi scored on an 18-yard run.
Stephen Skon, making his first career start after leading Georgetown over Princeton 21-20 last week, generated only 159 yards total offense for the Hoyas (3-2) compared to Brown's 361.
Alex Norocea kicked three Bears field goals.