Extra Innings Game (1877)

“….the St. Louis score being thereby tied, amidst loud applause, as an extra innings game was now looked forward to by the spectators, who like nothing better in a match than this.” Brooklyn Daily Eagle, September 13, 1877. p1

Previous earliest use (Dickson Baseball Dictionary, 3rd edition, 2009):
1ST USE. 1885 (Spalding’s Official Base Ball Guide, p. 19; Edward J. Nichols).