Harvard (2-0) has won the last eight games in the series, holding an 86-30-2 advantage dating to 1893.
Smith found a wide-open Henry Taylor for a 22-yard touchdown, giving Harvard a 7-3 lead. BJ Watson extended it to 14-3 on a career-long 43-yard run, and Cole Thompson returned his second career interception for a 27-yard score. Harvard made a goal-line stand at the end of the first half to preserve its 24-3 lead.
Harvard's first four drives of the second half ended in a missed field goal, two turnovers on downs and an interception. But the Crimson went on a 14-play, 87-yard scoring drive to extend its lead to 31-17.
Adam Scott caught a career-high eight passes for 90 yards and one score for Harvard. Justice Shelton-Mosley added six catches and 65 yards, moving into fourth in program history with 137 receptions.
Michael McGovern had 293 yards passing, two touchdowns and two second-quarter interceptions for Brown (0-2).
Sebastian Dovi intercepted a pass deep in Brown territory and the Bears went on a four-play, 88-yard drive - highlighted by Jakob Prall's catch-and-run for 55 yards - to pull to 24-17 with 12:24 to go.
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