The Mountain Hawks (7-0, 1-0) have won 15 straight regular-season games dating back to last season, good for the longest active streak in the Football Championship Subdivision.
Barket, who finished with 123 yards rushing, tied the game 7-7 with his 1-yard touchdown run.
Georgetown (3-4, 0-1) regained the lead, 14-7, behind Jeremy Moore's 80-yard interception return for a touchdown with 3:52 left in the first half. The Hoyas' defense forced turnovers (four interceptions, one fumble) on five of Lehigh's first eight possessions.
The Mountain Hawks' offense rallied in the second half, opening the third quarter with a 9-play, 76-yard scoring drive. Keith Sherman capped the drive with a 1-yard touchdown.
Peery's field goal with 10:58 remaining sealed the win.
South Carolina has decided to give up Saturday's home game against No. 7 LSU because of devastating floods that have hit the state, moving the game to Baton Rouge.
West Virginia All-Big 12 safety Karl Joseph is out for the remainder of the season after injuring his knee during a non-contact drill in Tuesday's practice.
Rutgers has reinstated senior wide receiver Leonte Carroo a day after an assault charge against him was dropped.
Ole Miss cornerback Tee Shepard, who missed all of last season with a toe injury, has decided to give up football and focus on completing his college degree.
Tennessee senior wide receiver Alton "Pig" Howard has been dismissed from the team for a violation of team rules, coach Butch Jones announced.
UCLA junior linebacker Myles Jack has withdrawn from school and will enter the NFL draft, making the decision just weeks after suffering a season-ending knee injury.