The game was actually looking fairly normal up through the 9th inning. The Red Wings were leading 1-0 off a run they'd scored in the top of the 7th. In the bottom of the 9th, however the Sox scored a run, to tie it up. What followed was 12 scoreless innings -- equivalent to one and one-third complete scoreless games!. In the top of the 21st, the Red Wings managed to score a run; unfortunately for them (and all the weary players) the Sox answered back with a run of their own in the bottom half of the inning. Play then continued for another 10 scoreless innings, until the umpires called the game at the end of the 32nd inning.
The resumption of the game was a bit of an anticlimax: the Sox scored a run in the bottom of the 33rd, and the longest game in professional baseball history was over, after 8 hours and 25 minutes.
The other interesting thing about that game is who participated in it. On the Pawtucket side, we have Wade Boggs, who would go on to have a great career with the Boston Red Sox (among others). On Rochester, we find Cal Ripken, Jr., who went on to play with the Baltimore Orioles and set the record for most consecutive games played. For the record, Boggs was 4 for 12, with 1 RBI, and Ripken went 2 for 13. When Boggs hit the single that tied it up in the bottom of the 21st, he recalls that "A lot of people were saying , 'Yeah, yeah, we tied it, we tied it!' And then they said, 'Oh, no, what did you do? We could have gone home!'"
With a little help from the Pawsox's web site: http://www.pawsox.com/team/longest_game/