The German came through 6-4 2-6 6-3 after two hours and 19 minutes of tennis at Flushing Meadows.
Both players broke twice in an evenly-matched opening set, but with the score at 4-4 it was Kerber who made a decisive third break before serving out the set.
Bouchard dominated the second set, breaking the world number nine in three consecutive service games to move 5-1 ahead. Despite losing the seventh game off her own serve, the Canadian broke Kerber once more to take the match into a deciding set.
Kerber regained her composure during the third set as she broke Bouchard's first service game to establish an early advantage.
In a dramatic ninth game, Bouchard saved four match points but Kerber held her nerve to wrap up the match at the fifth attempt.