In 2006, the Los Angeles Dodgers tied a game against the San Diego Padres, with four straight solo home runs in the 9th inning (after trailing 9-5). Then, in the 10th inning (trailing 10-9), a two-run walk-off homer by Nomar Garciaparra won it for the Dodgers.
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The scoreboard from this game shows that both teams hit a lot of base hits (H) and that the Los Angeles Dodgers made two defensive errors.
The longest game by innings (in the MLB) was a 26-inning game in 1920; the teams were tied 1-1 when the game was called because of darkness.