Perfect Game (1904)

Cy Young’s feat was not a record. But Boston club made one with his aid. Perfect baseball game.” (Headline) Rochester Democrat and Chronicle, May 8, 1904, p22
— Notes that it only tied the record, because two pitchers had previously done it.

Cy Young has twice pitched a perfect game.” (Headline). The Brooklyn Citizen, May 9, 1904, p4
— Lists previous “perfect games” but includes non-perfect no-hitters in the list.

Several others, as well. Hard to say when it started being used exclusively the way it is today. 

Previous earliest use (Dickson Baseball Dictionary, 3rd edition, 2009):
1ST USE. 1909. “[Ed] Walsh congratulated Addie Joss on the latter’s feat of pitching a perfect game [on Oct. 2, 1908]” (The Washington Post, Jan. 10).