The rest of the Kansas City offense ground up Rays starter Jeremy Hellickson.
Perez finished with four RBIs, Butler drove in three runs and Moustakas also drove in a pair as the Royals won their second straight following a seven-game slide.
"We're a good team. We're a good-hitting ballclub," Moustakas said. "We knew we'd be able to get to the pitcher early and score some runs."
Hellickson (10-8) allowed five runs in just 2 2/3 innings for Tampa Bay. It was the struggling right-hander's shortest start since June 30, 2012, when he went the same distance in a game against Detroit before getting pelted in the leg by a line drive.
"The offense to me looks like it is back on track," Royals manager Ned Yost said.
Guthrie (13-10) allowed six hits and three walks but twice delivered timely strikeouts. He fanned Kelly Johnson with two aboard to end the third inning, and then struck out David DeJesus on a called third strike to leave the bases loaded in the fourth.
Rays manager Joe Maddon argued that the call and was tossed by plate umpire Greg Gibson.
"It's been exasperating. They beat us up. We don't like Kansas City," Maddon said, "except for the food. The Plaza is nice and the barbeque, and this is one of the best ballparks in the American League, in all of baseball really, but they just beat us up."
James Loney drove in the only run for the Rays, who no doubt rued having to make the quick trip to Kansas City in the midst of a six-game homestand. They began the day a game back of the Red Sox in the AL East and lead the American League wild-card standings.
It seemed like a season ago when the teams first tried to play. The temperature was 41 degrees with a wind chill of 21 at first pitch on May 2, and Kauffman Stadium resembled a snow globe by the fourth inning as flurries fell. The game called with the Royals leading 1-0.
It was 93 degrees at first pitch Monday, making for a 52-degree difference from the original date. Sunny skies and a slight breeze made it feel even warmer.
The biggest subplot to the game wasn't the weather, though, but the return of Myers to Kansas City. The former minor league player of the year was the key to a seven-player trade last December that netted the Royals starting pitchers James Shields and Wade Davis.
Myers hadn't played at the K since the All-Star Futures Game in 2012, when he went 2 for 4 and drove in the three runs. He didn't fare nearly as well against big league pitching, either: He went 0 for 4 with two strikeouts, slamming his bat down after a pop out in the fifth inning.
"The fans kinds of wore me out in right field," he said, "otherwise it was good."
The Royals struck first on Butler's RBI single in the first, but they didn't really break through until the third inning. Three straight hits and a walk scored two runs, a sacrifice fly added another, and Justin Maxwell's RBI single helped drive Hellickson from the game.
Hellickson fell to 0-5 in his last six starts. He's made it through five innings once.
"It's very frustrating when you don't give your team a chance to win at all, 5-0 in the third," he said. "You don't give them a chance to come back."
The Royals tacked on five more runs in the sixth against the Tampa Bay bullpen, highlighted by Perez's three-run shot. That was more than enough help for the Royals' relief corps, which put together four shutout innings to end Guthrie's three-game losing streak.
"I created some problems for myself," Guthrie said. "The bats picked us up fortunately and we won it pretty easily, even though it was a struggle early."
Royals RHP Luke Hochevar was absent after his wife gave birth to a daughter Sunday. Hochever will rejoin the club Wednesday in Minnesota. RHP Will Smith took his place on the 25-man roster. ... Rays LHP Matt Moore (sore left elbow) remains on track to start a minor league game Thursday. He could rejoin Tampa Bay at the Angles on Sept. 3. ... Rays OF Jason Bourgeois cleared waivers and accepted an outright assignment to Triple-A Durham.