Left-hander Jason Vargas (10-3, 2.27 ERA) picked up his Major League-leading 10th win of the season, allowing three runs on eight hits and two walks over six innings.
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The Angels took a 2-0 lead in the opening frame on an RBI double by Kole Calhoun and a one-run single by Andrelton Simmons, however starter JC Ramirez (6-5, 4.59) was unable to hold the lead, relinquishing five runs on five hits and four walks across three-plus innings.
Ramirez, who recorded six strikeouts on 89 pitches Sunday, was more concerned with his high pitch count than content with the number of batters he fanned.
"I want to go six and seven innings," he said. "I think it wasn't a bad start, I just threw a lot of pitches."
Royals third baseman Mike Moustakas hit a three-RBI double in the top of the third to give Kansas City a 3-2 advantage. In the fourth, first baseman Eric Hosmer lifted a sacrifice fly and Salvador Perez launched a three-run homer the following at-bat, pushing the Royals ahead, 7-2.
"They got two, big two-out hits -- one by Moustakas and one by Perez," said Angels manager Mike Scioscia. "Really set the tone for the whole game, really."
Hosmer's RBI marked the 500th of his career.
"To reach 500 is a tremendous honor, especially nowadays with the pitching as good as it is," Hosmer said. "Obviously, you can't do it without guys getting on in front of you."
The win moves the Royals, who complete their West Coast road trip 7-2, to 33-35. Meanwhile, the Angels drop to 36-37, and are 10-10 since Mike Trout hit the disabled list with a thumb injury May 29.
Royals manager Ned Yost was asked if the recent surge might get attention from around the league.
"I don't really care if people look at us or not," Yost said. "We feel good about our team. In years when we [got to the World Series] we haven't had people look at us like we're very good. We've learned not to pay attention to it. We just go out and play as hard as we can and try to win ballgames."
MOMENTS THAT MATTERED
Perez redeems himself: Perez gave Kansas City a commanding 7-2 lead when he drilled a three-run homer off Angels reliever Keynan Middleton in the top of the fourth. In a bases-loaded situation in the third inning, Perez flied out to right field leaving the runners stranded.
Vargas survives: In the bottom of the sixth, Vargas allowed the first three batters of the inning to load the bases with none out. However, the left-hander buckled down, forcing a sac fly and two popouts to keep Kansas City in control, up 7-3.
"He started laboring and had the bases loaded and none out, but did what he does best - limit the damage," Yost said.
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Andrelton Simmons set a career-high when he swiped his 11th stolen base of the season in the bottom of the first inning. Simmons only needed 72 appearances to pass the 10 stolen bases he recorded in 124 games last season.
UPON FURTHER REVIEW
Calhoun laced an RBI double that bounced off the top of the right field to give the Angels a 1-0 lead in the first. The crew chief reviewed the play, but officials confirmed that the ball stayed in the park, and Calhoun remained at second base.
"It looked like it was worth reviewing, for sure," Scioscia said of the play. "I couldn't tell exactly if it had scraped the wall coming back from out, scraped the side wall. ... I think that's about as close as you can come to a home run without getting one."
Royals: Right-hander Jason Hammel (3-6, 5.05 ERA) takes the mound for the Royals as they return home to face Boston at 7:15 p.m. CT. Hammel gave up one run over 6 2/3 innings in the Royals' 7-2 win over the Giants on Wednesday.
Angels:Rookie right-hander Parker Bridwell (1-0, 2.19 ERA) will toe the rubber for the Angels on Tuesday, when they open a three-game series against New York at 4:05 p.m. PT. Bridwell is starting in place of right-hander Matt Shoemaker, who was placed on the 10-day disabled list on June 15 with a strained right forearm extensor.
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Kaelen Jones is a reporter for MLB.com based in Los Angeles.
This story was not subject to the approval of Major League Baseball or its clubs.