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.
Ohio State remained No. 1 in the AP Top 25 and tied a poll record Sunday despite lagging support from voters. Meanwhile, No. 2 TCU and No. 3 Baylor edged forward and No. 4 Michigan State slipped.
Texas cornerback Kris Boyd has apologized for retweeting a Texas A&M fan during halftime of Texas' 50-7 loss to TCU on Saturday.
The Big 12 on Sunday acknowledged an officiating mistake that incorrectly awarded Oklahoma State a first down Saturday and said the officials involved would be disciplined.
Georgia coach Mark Richt says he's sticking with Greyson Lambert, who was just 10-for-24 for 86 yards in a loss to Alabama, as the Bulldogs starting quarterback.
Will Grier threw four touchdown passes to four receivers -- all in the first half -- and No. 25 Florida downed third-ranked Mississippi 38-10 on Saturday night.
Leonard Fournette highlighted his SEC-record third straight 200-yard game with a 75-yard touchdown run, and No. 9 LSU overcame Eastern Michigan 44-22 on Saturday night.