The Crimson (6-1, 3-1 Ivy League) held a 13-0 lead in the second quarter as Conner Hempel ran for a nine-yard score and Flesher kicked two field goals.
Ricky Zorn threw a 32-yard strike to Andrew Berg on a trick play and Harvard converted the 2-point conversion. Dartmouth knotted it up with a seven-yard score by Kyle Bramble late in the third quarter.
Harvard drove 56 yards on 13 plays before setting up Flesher's game-winner with 48 seconds remaining.
Notre Dame lineman Parker Boudreaux was hospitalized Sunday for an unknown condition and will remain there for "2-3 more days," he said on Twitter.
Three of the Tigers' first four games are against Clemson, Texas A&M and LSU. If they can come out of it, say, 3-1, they might contend in the SEC West.
Wisconsin will be up against a powerful LSU defense, directed by former Badgers coordinator Dave Aranda, in the season opener at Lambeau Field.
Mason Rudolph is a proven winner who transformed Oklahoma State's offense as soon as he stepped on the field.
GameDay 100: With just seconds left in the game, Michael Crabtree catches a touchdown pass to win the game for Texas Tech over Texas.
Wolfpack all-purpose threat Nyheim Hines will enter his sophomore season off a successful track season that he says will propel him to more heights.