Wrigley Field actually opened two years before the Cubs moved in, in 1914, under the name of Weegham Field. The Chicago Whales played there for two years, and actually won the Federal League championship in 1915. They didn't play a post-season, though.
Since the Cubs moved into Wrigley, they managed only one post-season series win, in 13 tries. That was in 2003, against the Atlanta Braves, but the clinching game was in Atlanta. They went on to lose the next series to the Florida (now Miami) Marlins.
This year, the Cubs played their arch-rivals in the NL Central division, the St Louis Cardinals. The Cardinals have been in 45 postseason series since the Cubs took up residence in Wrigley, and won 29 of them.
Last night, the Cubs finally won a post-season series at home in Wrigley Field. For Cubs fans, the win is the most important thing...but having it happen at home, against those Cardinals, made it just a little bit sweeter.