Aviles' blast, which landed in the Indians' center-field bullpen, was estimated at 412 feet. It came on a 1-1 pitch from right-hander Fausto Carmona with the bases empty.
"It's awesome, I'll take it," said Aviles, who wasn't aware of the homer's numerical significance. "It would've been nicer if we'd have gotten the win."
The drive gave the Royals a 2-0 lead in a game they lost to the Indians, 5-3.
Home run No. 1 was hit on April 13, 1969, by Mike Fiore. He was the first of 255 players to sock homers for the Royals. George Brett had the most (317), and Steve Balboni holds the single-season mark (36), set in 1985.