"We've got the bats going -- swinging and hitting the long ball. Big for us," manager Ned Yost said.
The Royals had six homers in the sweep, including three on Wednesday. Butler's blast was preceded by two other solo shots, by Mike Moustakas in the first inning and by Alcides Escobar in the third inning.
Butler's deciding blow came as the Royals were running low on stamina and able bodies in the bullpen during the oppressive heat. The Rays had just tied the game in the top of the eighth and Yost wasn't relishing extra innings.
"They were getting bags of IV fluid lined up in the training room," Yost said.
Right-hander Burke Badenhop had just relieved Rays starter Matt Moore with one out in the eighth, when Butler caught hold of a 2-1 pitch and drove it over the left-field wall for his 15th homer.
Butler remembered facing Badenhop in 2008 when the sinkerballer was with the Marlins.
"The only thing I knew was he had a sinker and a slider. And I knew the velocity," Butler said. "[The pitch] was a sinker up, so it just kind of ran and that's how I got underneath it. ... That's what you want from a sinkerball guy, an elevated pitch."
The ball bounced off a fan's hands just over the 387-foot mark.
This was the Royals' third series sweep this season and first over the Rays since 2001. They also swept a two-game series at Texas and won all three from Milwaukee in Kansas City.
Everett Teaford, called up from Omaha to make this start, held the Rays scoreless through the first five innings, but the sixth began with B.J. Upton's walk and Carlos Pena's single.
"He got through five and he just kind of ran out of gas," Yost said.
No argument from Teaford. He knew he'd hit the wall as the sun beat down.
"Being honest, yes," Teaford said. "But I've got to get through that. I got the ground ball, but Pena just hit it in a good spot."
When Teaford left he had a 4-0 lead, the last two runs coming in the fifth inning off left-hander Matt Moore on Yuniesky Betancourt's bouncing single.
Kelvin Herrera relieved him and, before the inning was over, yielded a couple of RBI singles to Jeff Keppinger and Ben Zobrist that cut the Royals' lead to 4-2.
The Royals' normally sharp bullpen didn't look fresh in the heat. Greg Holland wiggled through a tough seventh. Then, Tim Collins gave up the two tying runs in the eighth.
"They've been used a lot and they've been going through that little dead-arm period where they're struggling with their command," Yost said.
Anyway, the Rays' eighth began with an error as Pena's grounder deflected off first baseman Eric Hosmer's glove and caught first-base umpire Brian Gorman in the face, opening a small cut next to his nose. The blood was wiped away as Gorman was treated during a brief delay and stayed on the field.
After a walk and an out, Zobrist drilled a two-run triple to right field, ending Collins' stay in favor of Aaron Crow. Pinch-hitter Will Rhymes grounded to Escobar, drawn in at shortstop, and Zobrist's bid to score the go-ahead run was thwarted by the throw home to catcher Salvador Perez.
There was a brief scare, though, as Zobrist slid into Perez's surgically-repaired left knee, and left the catcher kneeling uncertainly in the dirt. As Perez made the tag, Zobrist's spikes caught between the catcher's shin guard and his knee, causing some concern. After being checked by a trainer, Perez stayed in the game.
"It's just a bruise on his knee," Yost said. "He's fine."
Crow got out of the inning, Butler hit his home run and closer Jonathan Broxton worked the ninth for his 18th save.
"That was a huge home run, because it enabled us to bring in Broxton right then and there," Yost said.
Typically, Broxton heightened the suspense with a one-out walk before ending the game on a double-play grounder.
"Still not 1-2-3," Broxton said with a chuckle.
The victory left the Royals just five games under .500 with something to pursue before the All-Star extravaganza begins in Kansas City. Before then, they have four games at Minnesota, four games at Toronto and three at Detroit.
"Our goal from the end of the 12-game losing streak was to get back to .500 by the All-Star break," Yost said. "That's been our goal since April."
They got one game closer to that goal thanks to Butler's home run. And they got out of the heat, which was starting to cause players to cramp up.
"When he hit that I was just hoping it had enough height to get out, because he hit it on the dead line and, luckily, it did," Yost said.