“The Philadelphia nine are evidently playing a very strong game out West, and by it they are rapidly improving their position on the pennant race.” Brooklyn Daily Eagle, June 25, 1875, p6
Previous earliest use (Dickson Baseball Dictionary, 3rd edition, 2009):
1ST USE. 1876. “For the first time since May last the Hartford have been obliged to take third place in the pennant race” (Brooklyn Eagle, July 24; Peter Morris).