5/09/1984 - White Sox beat Brewers in 25
The Chicago White Sox beat the Milwaukee Brewers 7-6 after 25 innings of baseball. The game finished one inning shy of the record for most innings -- in 1920, the Boston Braves and Brooklyn Dodgers played 26 innings before the game was called a tie due to darkness. The Brewers/White Sox game did set the record for the longest game in terms of time: 8 hours and 6 minutes.
It actually began the night before at 7:30 PM and was halted at 1 AM with the score tied at 3-3 in the 17th inning. It picked up the next day and went another eight innings. Remarkably, both teams scored three runs in the 21st inning to extend the game. The marathon only came to an end in the 25th when Harold Baines knocked out a solo home run.
Getting the win in the 25th inning was Tom Seaver. He then started and won the White Sox' regularly scheduled game that day.