Wilson struck out the side in the first inning and finished with five strikeouts as he surrendered just three hits and no walks. Wilson signed a five-year, $77.5-million deal with the Angels and, so far in four starts, he has a 0.64 ERA.
The Royals broke a 4-4 tie in the eighth inning with two runs. Chris Getz singled against right-hander Ryan Brasier, who subsequently left with an injury after one out. Non-roster player Brian Fletcher delivered a run-scoring double off reliever Daniel Tillman and scored on Mitch Maier's single and an error.
This was the first Cactus League matchup between the Royals and Angels, who'll be Opening Day opponents on April 6 at Anaheim.
Eric Hosmer struck out twice against Wilson as he faced him for the first time in his career.
"He looked good," Hosmer said. "He was attacking with the fastball but, to take some positive from the day, we got some good looks off of him to get ready for that first weekend."
The Angels got one run off Royals starter Felipe Paulino in his four innings. Mark Trumbo doubled off the right-field wall in the second inning and later scored while Maicer Izturis, who had singled him to third, was put out in a rundown on a steal attempt.
Paulino twice struck out the Angels' other big offseason investment, first baseman Albert Pujols. He also fanned against Louis Coleman and was 0-for-4, but he's still hitting .367.
Reliever Jonathan Broxton ran into his first snag as a Royal, surrendering two runs in the fifth inning on three hits, including Erick Aybar's RBI double that was lost in the sun. Broxton's error made one of the runs unearned.
The Royals rallied with four runs in the sixth against right-hander Jordan Walden, who gave up five hits in his one-third inning. Hosmer and Jeff Francoeur had RBI singles, Billy Butler banged a run-scoring double and another run scored on a wild pitch.
Coleman gave up a solo home run to Vernon Wells in the eighth inning that gave the Angels a 4-4 tie.
Angels prized prospect Mike Trout made his spring debut after being derailed by an illness. He went 0-for-3 with a walk as the designated hitter, getting caught stealing his lone time on base.
Up next for Royals: Luis Mendoza will try to expand on his marvelous Cactus League record when he starts against the Oakland A's at 3:05 p.m. CT on Wednesday at Surprise Stadium. Mendoza has given up just one earned run in 10 2/3 innings, running up 11 strikeouts as he tries to secure a rotation job. He's to be followed by relievers Tim Collins, Jose Mijares, Jeremy Jeffress, Greg Holland and Francisley Bueno.
Dick Kaegel is a reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.