Seven games were played, which means that the teams split the first six games, each team winning three games. It does not matter who won each of the first six games, since neither team had yet to win four games. The winner of game 7 will have won four games, and therefore, the World Series.
The team that hosts the first two games also hosts the last two games. Since Los Angeles hosted the first two games, game 7 was in Los Angeles. In baseball, the home team bats last. Los Angeles batted last in game 7. Since game 7 went 13 innings, Los Angeles would have batted in the bottom of the inning. In this situation, the home team can never win by more than four runs. When the home team bats in the last inning, the game ends as soon as the winning run is scored. The only way the home team can win by more than one run is via a home run, in which case all runners on base at the time can score. A grand slam home run would only provide a margin of four runs. Therefore, the home team's margin of victory in an extra-inning game can never exceed four runs. The final score was 13 to 8, a margin of five runs. Los Angeles, being the home team, could not have won by that margin. The game was tied 8 to 8 going into the 13th inning. New York scored five runs in the top of the 13th inning.
Therefore, the New York Yankees won the World Series, four games to three.
Today's brain teaser courtesy of Braingle.com.