MINNEAPOLIS — Jim Thome has been plagued by aches and pains for the better part of a decade. They just seem to be coming around a little more often in his 19th season.

A strained oblique and bothersome toe injury on his left foot have slowed his chase of 600 career homers, but the Minnesota Twins are sticking with him for moments like the sixth inning on Sunday against Kansas City.

With the game tied and his team in desperate need of a jolt, Thome hit his 596th home run to lift the Twins to a 4-3 victory over the Royals.

Thome’s tiebreaking three-run drive off Felipe Paulino soared into the upper deck in right-center field, leaving him four shy of becoming the eighth player to hit 600 home runs.

“It’s always special,” Thome said. “That feeling you want to kind of last forever. It went out, it put us ahead. And that’s No. 1.”

Jeff Francoeur homered and Melky Cabrera added two hits for the Royals. Paulino (1-3) struck out eight in seven innings, yielding four runs and seven hits.

Brian Duensing (7-7) gave up three runs and seven hits in 6 1-3 innings for the Twins, who started a crucial 12-game homestand by taking three of four from the Royals.

After a relatively healthy season last year in which he hit 25 homers in 108 games, this one has been a tough one. He will turn 41 in August, and it’s getting tougher and tougher to get his body ready to grind out each at-bat.

On a sweltering day where the heat index climbed past 110 degrees, Thome looked plenty loose when he sent a 3-2 pitch from Paulino an estimated 490 feet into the stands for a 4-1 lead. He also became the 11th player to hit 500 homers in the American League, according to STATS, LLC.

“He’s had some injuries and we know we have to limit what you can do with him to keep him healthy,” Twins manager Ron Gardenhire said. “That was a big at-bat and it was one mistake. That’s what those guys do. You make one mistake and he’s going to put it in the seats. That’s why he’s got that many home runs.”

Francoeur came back with a two-run shot of his own in the top of the seventh, but Glen Perkins pitched a perfect eighth and Joe Nathan, who resumed his closer role when Matt Capps began to struggle, picked up his fifth save of the season.

It was a tough loss for Paulino, who has pitched well since joining the Royals at the end of May. Paulino hit 97 mph on the Target Field radar gun. He only walked one hitter, an intentional pass for Joe Mauer, who had two hits and an RBI.

“We’re at the point where one mistake kills us,” Royals manager Ned Yost said. “We’re just walking a thin line. Just keep battling through it. We’re getting better. We’ve just got to keep trudging through it.”

The Royals made Duensing work through the first three innings.

The Twins left-hander needed 58 pitches to get to the fourth, giving up an RBI single to Alex Gordon to fall behind in the first inning. But he breezed through innings four, five and six, averaging just 10 pitches per frame to keep the Twins in it.

Gardenhire returned to the ballpark Sunday after missing Saturday’s game with a chest cold that has bothered him for weeks. He played it safe by watching the game from the air-conditioned clubhouse, while bench coach Scott Ullger made the pitching changes

Paulino fanned Thome and got him to ground into a double play the first two times up. But he left a slider out over the middle of the plate in the third at-bat, and paid for it.

“He knows what his game’s all about,” Nathan said. “He came to us and pretty much said, ‘There’s going to be a lot of times I strike out. There’s going to be a lot of times I walk and there’s going to be a lot of times that I’m going to barrel one up.’

“We got to see a lot of that today. He punched out, but he also got to barrel one up and we got to see one fly a long way.”