One Game Playoff Games since 1995 (winners in bold)
1995 AL West: Angels @ Mariners(9-1)
1998 NL Wild Card: Giants @ Cubs(5-3)
1999 NL Wild Card: Mets (5-0) @ Reds
2007 NL West: Padres @ Rockies (9-8; 13 inn)
2008 AL Central: Twins @ White Sox (1-0)
2009 AL Central: Tigers @ Twins (6-5; 12 inn)
As of right now, there still could be two one game playoffs (Braves need to win in extra innings; Red Sox and Rays still playing), which would be a first (Rays and Cardinals would host if the games are played). The Braves have an extremely difficult game ahead of them in St. Louis if they should force it. Both teams will be under extreme pressure, but it will be like playing game 7 of the World Series (or the LCS) on the road, which teams almost never win.
To be fair, the last three, which have all been won by the home team, have all been one run games and two have gone to extra innings. They tend to be close, but it will be an uphill battle for the Braves or Red Sox if the games are played.