Georgetown (4-1) has won four straight and opens Patriot League play hosting Fordham on Saturday. The Big Red (1-2) travel to Harvard on Saturday.
Crayton caught his only pass for a score with 5:13 remaining. The Hoyas forced a three-and-out on Cornell's next possession. Johnson threw a 9-yard pass to Joshua Tomas on fourth-and-8 with 3:34 to play and Georgetown ran out the clock.
Johnson was 6 of 9 for 110 yards passing, and ran for a 3-yard touchdown in the first quarter. Herman Moultrie III added 101 yards rushing on 24 carries for the Hoyas.
Harold Coles ran for a 5-yard touchdown at the end of the third quarter for Cornell (1-2). Coles finished with 65 yards rushing.
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