The World Series champion Royals have lost eight of 10.
Ramirez delivered a bases-loaded double in the third and a two-run double in the fifth. He singled in the second, walked in the eighth and raised his batting average to .324.
Danny Salazar (3-2) held the Royals to four hits and struck out nine in 7 2/3 innings.
Yordano Ventura (2-2) allowed five runs and threw 97 pitches in four innings. The right-hander walked five, increasing his AL-leading total to 25.