"We're there," said Florida's manager, Jim Leyland, after Tuesday's decisive 7-4 victory. "I told our club all along that I thought we were one club that could beat the Atlanta Braves."
The Marlins scored four times in the first inning against Tom Glavine and held on to win the series 4-2.
Florida, who entered the league in 1993, eclipsed the mark of eight years set by the 1969 New York Mets for quickest expansion team to reach the World Series, doing it in its fifth season.
The upstart Marlins will face the winners of the American League Championship Series between the Cleveland Indians and Baltimore Orioles, with Games 1 and 2 of the World Series in Miami on Saturday and Sunday. Cleveland leads Baltimore 3-1.
Brown (2-0), scratched from one start and pushed back from another due to a viral infection, scattered 11 hits, but only three after the fourth inning. He walked one and struck out eight while throwing 140 pitches.
"This is not about me," said Brown, who persuaded Leyland to leave him in the game in the seventh inning when the manager was about to pull him. "What I had to do is nothing compared to what this team has done all year long."
Leyland's Pittsburgh Pirates lost National League Championship Series to Cincinnati in 1990 and the Braves in 1991 and 1992. One of his top players with the Pirates was his current third baseman, Bobby Bonilla.
The pair wept together on the field after the game. "It was a great deal of emotion." Bonilla said. "It took a long time to get here. I'm glad it was with Jim Leyland."
The Marlins were the National League wild card, finishing behind the Braves in the Eastern Division but beating them eight times in 12 games during the regular season.