Left-hander Alex Wood, also expected to be a No. 4 starter, went four innings for the Dodgers and gave up six hits and three runs, while walking none and striking out four.
Salvador Perez drove in two runs for the Royals, one on a groundout to plate Kendrys Morales, and another on a towering home run to left field.
The Dodgers didn't get their first hit until right fielder Rico Noel doubled to right off left-hander Scott Alexander with one out in the fifth to score Rob Segedin from first base.