The Bison led 16-10 at the half but Georgetown scored on an 81-yard drive at the start of the fourth to go up by one point. After forcing the Hoyas to go three-and-out, Bucknell drove down 55 yards in eight plays and RJ Nitti capped the drive with the TD pass to Carter.
Georgetown got the ball with 6:53 left on the clock, but advanced just four yards in five plays and was forced to punt.
Carter finished with six receptions for 77 yards, and CJ Williams added 136 yards and two touchdowns on the ground for the Bison (6-1, 2-0 Patriot League).
Kyle Nolan threw for one touchdown and ran for another for the Hoyas (2-6, 0-3).