The victory was the first for new Bulldogs coach Tony Reno.
The Hoyas (2-1), driving from their own 25, had first-and-10 on the Yale 17 when Bibb picked off an Aaron Aiken pass with 33 seconds remaining.
The Bulldogs, who have won six straight season openers against Georgetown, opened the scoring on Varga's 2-yard TD, capping a 90-yard drive.
Claytor Dalen gave Georgetown a 21-17 lead on a 32-yard rush, but Varga's 9-yard run put the Bulldogs ahead for good.
Western Kentucky commit Jared Nash launches this snap from the bleachers and successfully sinks it in the garbage can.
Florida State coach Jimbo Fisher hopes quarterback Sean Maguire is ready to go full speed by the middle of June.
Graduate transfer quarterback Davis Webb has officially joined California, giving the Golden Bears an experienced option to replace No. 1 overall NFL draft pick Jared Goff.
First-year football coach Dino Babers, hired by former Syracuse AD Mark Coyle, is on the committee that will search for Coyle's replacement.
Hugh Freeze has some major holes to fill on offense with the departures of Laremy Tunsil and Laquon Treadwell, but there is Chady Kelly and good depth.
After transferring in from Montana State, Dakota Prukop has a checklist he's working from as he prepares to compete for the Oregon job.