“The boys struck a winning streak in the west and there was a great desire to have it continued on the home grounds.” The Times [Philadelphia}, July 11, 1886, p11
Previous earliest use (Dickson Baseball Dictionary, 3rd edition, 2009):
1ST USE. 1889. “The Browns kept up their winning streak at Louisville yesterday, when they defeated the home team by a score of 13 to 6” (St. Louis Post-Dispatch, Apr. 23; Peter Morris).