Hiroki Kuroda opposed Paulino, who was making his season debut upon his return from the DL, and threw just four and one thirds innings for New York before being pulled. He allowed six hits and three runs, and dropped to 2-4 on the season.
Designated hitter Billy Butler led the Royals offensive charge, knocking in three RBI's on the evening.
Russell Martin and Curtis Granderson combined for five of the eight Yankees hits, although the team was unable to convert in nine at-bats with runners in scoring position.
The two will finish off their series on Sunday afternoon at Kauffman Stadium, and New York will aim to earn a series split when Phil Hughes takes the mound for the Yankees against Luke Hochevar.
See Pinstripe Alley for more discussion and analysis of the Yankees. Check back with SB Nation New York for more information about Mariano Rivera's injury.