Paul Dickson's BASEBALL DICTIONARY says this is "the last and deciding

game of a series when the previous games have been split." No citations or

dates are given in the entry. The term may or may not come from poker.

This is from the Chicago Times, 12 September 1886, pg. 5, col. 2:

WON THE RUBBER./Chicago's Base-Ball Artists Take the Deciding Game from

the Detroit Players.