Shutout (1879)

“The Twinklers are very happy to-night over their shutout of the Grays in the ninth contest.” Cincinnati Enquirer, August 22, 1879, p8 (“Syracuse 6; Providence, 0”) [Ken Liss]

Previous earliest use (Dickson Baseball Dictionary, 3rd edition, 2009):
1ST USE. 1883. “It looked very much like a shut-out, but the boys went up with a determination to avert such a calamity if possible, and it was” (Detroit Free Press, May 4; Peter Morris).