Lehigh dominated Princeton in the first half. Barket ran for five yards to score the first points of the game and Sherman's 2-yard run with 3:34 in the second quarter gave Lehigh a commanding 17-0 halftime lead.
Princeton, which has lost three straight season openers to Lehigh, rallied in the fourth quarter. The Tigers cut the lead to 17-14 with 4:54 to play on Akil Sharp's second rushing touchdown.
The Mountain Hawks' defense then stiffened, forcing a three-and-out on Princeton's next possession. Lehigh sealed the win, converting on third down-and-11 when quarterback Michael Colvin connected with Dylan Colgate for 27 yards.
Michael Colvin finished 21 of 34 for 276 yards passing for Lehigh (3-0).