The Royals led 4-0 in the third Friday night, then 5-1 in the fifth, before the Orioles pulled even in the sixth as a steady rain fell.
In the ninth, after midnight, Kansas City loaded the bases with no outs, but Eric Hosmer hit into a forceout at home, helped by catcher Nick Hundley's slick pickup at the plate, and Billy Butler grounded into a double play.
In these playoffs, the Royals became the first major league team to win three consecutive extra-inning postseason games. They beat the Athletics in the wild-card game in 12 innings, then won each of the first two games of their ALDS sweep of the Angels in 11.
Game 2 is scheduled for Saturday afternoon.