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.
A UCLA football player was suspended indefinitely Friday after he was arrested on suspicion of rape.
The tougher tests await down the road for No. 3 Baylor Bears, but coach Art Briles has seen enough of his Bears to know this is his best team.
A decision has been made that Randy Edsall will not be the football coach at Maryland next season, and discussions are taking place about how and when to separate, a source said Thursday night.
Appalachian State's board of trustees has approved a five-year contract for third-year football coach Scott Satterfield, who guided the Mountaineers through the transition from FCS to FBS.
Florida State running back Mario Pender has been released from the hospital but could be given a medical redshirt if he cannot return to the field this season.
The University of Wisconsin agreed to a 10-year deal with Under Armour on Friday worth a total of $96 million in cash and the retail value of products received.