Royals manager Ned Yost said Young "was awesome. Really good."
"The good thing about him was we wanted to get his pitch count to 75. He got to 78. He got that [first] out in the fifth inning. I went out and told him, "Cy, you've exceeded your pitch count. [Pitching coach] Dave [Eiland] is getting a little nervous.
"And Chris says, 'Does Dave know I'm throwing a no-hitter?'"
Young, of course, was joking.
"I felt really good, though," Young said.
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.
Right-hander Joakim Soria threw his fourth straight scoreless inning this spring for the Royals.
Royals up next: The Royals travel to Goodyear for a 3:05 p.m. CT start against the division-rival Indians. Right-hander Kris Medlen will start for the Royals, followed by Wade Davis, Luke Hochevar, Chien-Ming Wang, Peter Moylan and David Huff.
Dodgers up next: After a day off on Wednesday, Clayton Kershaw -- who has dealt with a foul bunt off his foot and a rear-end fender bender in the last few days -- starts for the Dodgers against Trevor Bauer and the Indians Thursday night in a 7:05 p.m. PT start in Goodyear. Scott Van Slyke, who has missed three games with a sore hip flexor, is expected to return to game action.