The Chicago Cubs have never beaten a New York team in the post-season. The Cubs were swept by the Yankees in the 1932 World Series, and again in the 1938 series. They are 0-2 thus far in the 2015 NLCS.
They did actually defeat the Giants in the one game playoff in 1908 which gave them the NL Championship. Whether that is considered the post season, I'm not sure. I'm still not sure if the is season's Wild Card game is considered post season baseball or merely a "play in" game.