Perez is now hitting .474 (18-for-38) in his career against Verlander.
"He's a great pitcher, and I don't know any secret," Perez said. "I'm just up there trying to do my job and he's trying to do his job. Today he left a couple fastballs up, and I was able to hit them."
Verlander (1-4) struggled in his ninth start of the season, allowing five runs on 10 hits in seven innings. He didn't walk a batter for a career-best third straight start, but the Tigers are now 1-8 in his outings this year.
The game was overshadowed by an afternoon announcement that Dave Dombrowski was being replaced as Detroit's general manager by his top assistant, Al Avila. In 14 years with the Tigers, Dombrowski took one of the worst franchises in the game and took it to six postseason appearances including World Series losses in 2006 and 2012.
Detroit came into the season looking for a fifth straight AL Central title, but now trail the Royals by 12 1/2 games.
"It is strange to come here and see some of their big guys gone and then to hear about Dave Dombrowski," said Eric Hosmer, who scored twice, both on Perez RBIs. "That has to be really tough for them, especially after the last few years."
Danny Duffy (5-5) allowed one run on five hits and four walks in seven innings, only striking out two.
"Danny was outstanding tonight," Royals manager Ned Yost said. "
After Perez drove in Kansas City's first three runs, former Tiger Omar Infante doubled to lead off the fifth, took third on Alcides Escobar's sacrifice fly and scored on Ben Zobrist's sacrifice fly to deep right.
"That was huge," Yost said. "With that offense, you don't want to give them anything that lets them get back into the game."
Detroit threatened again in the seventh, as Nick Castellanos led off with a triple and Jefry Marte followed with a walk. Gose grounded to third baseman Mike Moustakas, who looked Castellanos back to the base before throwing to second for the force.
Castellanos then broke for the plate, and Omar Infante threw home to easily retire him and end the threat.
"My initial reaction was that if he wanted to go to the plate I was a sitting duck," Castellanos said. "Then when I saw that he was turning two, then I decided to go. I should have just taken off as soon as he hit it."
Royals: Duffy continued to pitch very well since returning from the disabled list with biceps tendinits. Duffy is 3-2 with a 2.66 ERA in eight starts since returning from the injury in late June.
Tigers: LHP Kyle Lobstein (shoulder) threw on the side with Triple-A Toledo. Lobstein, who has been out since May 24, is expected to begin a rehab stint with the Mud Hens this week. ... Tigers manager Brad Ausmus did not have any update on Miguel Cabrera (calf), who has begun agility drills in advance of an expected return later this month.
The teams play the second of their three-game series Wednesday afternoon, with both teams pitching deadline acquisitions. Johnny Cueto (7-6, 2.70) makes his second start for the Royals, while Matt Boyd (0-2, 14.85) will make his Tigers debut after being acquired for David Price. In Boyd's last major-league start — the second of his career — he faced seven Red Sox without retiring a batter.
Verlander came into the game with a 31-1 record in 37 career starts where he didn't walk a batter. His only previous loss came to the White Sox on August 11, 2006.