The most runs scored in a MLB playoff game is 30 (both teams runs combined). Boston (23 runs) won against Cleveland (7 runs) in Game 4 of the 1999 American League (AM) division series.
This is also most runs scored by one team in a playoff game (23).
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Both the Texas Rangers (2011) and the Atlanta Braves (1996) have scored fifteen runs in a MLB post-season game. The former is also tied for the most total runs by both teams scored in such a game, with Boston and Cleveland in 1999.
On June 29th 1897 the Chicago Colts Win 36-7 over the Louisville Colonels. Also, the 2nd most runs in a game was On August 22nd 2007 As Texas Rangers Win 30-3 Over the Baltimore Orioles
in 1897 the Chicago Colts scored 36. The modern day record is 30 by the Texas Rangers in 2007 against the Orioles They won the game 30-3. Go RANGERS!!