MINNEAPOLIS (AP) - Felipe Paulino's fastball was hitting 97 mph, and he was sprinkling in a nice changeup and sharp slider to keep the Minnesota Twins off balance through five innings.

Then one of those sliders flattened out at the worst possible time, and that's all it took for Jim Thome to spoil the emerging right-hander's otherwise sparkling start.

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Thome hit his 596th career home run, a three-run shot in the sixth inning, and the Kansas City Royals lost 4-3 to Minnesota on Sunday.

Thome's tiebreaking three-run drive into the upper deck in right-center field leaves him four shy of becoming the eighth player to hit 600 homers.

``We're at the point where one mistake kills us,' said manager Ned Yost, whose fading Royals have lost six of eight. ``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.'

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.

Paulino has been a source of hope for the eternally rebuilding Royals. He was 0-4 with a 7.36 ERA when the Colorado Rockies cut him loose in May. Since joining the Royals, Paulino has snapped a 33-outing winless streak and fanned 32 batters in his last four starts.

Even after taking the loss, Paulino and the Royals came away feeling pretty good.

``The Royals believe in myself,' Paulino said. ``You can see how my career right now is changing for the better. I'm a better pitcher.'

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.

Thome will turn 41 in August, and his 19th season in the big leagues has been a tough one. He's battled an oblique injury and a problem with a toe on his left foot, not to mention the aching back that has bothered him for the better part of the last decade.

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 has a great arm,' Thome said. ``I was very impressed with his stuff.'

Not good enough to sneak a mistake past one of the best power hitters the game has ever seen. The estimated distance made it the longest homer at second-year Target Field.

``I threw the pitch where it was supposed to be, it was just bad location,' Paulino said. ``It's what happens. The ball went right down the middle. It wasn't cheap. Not from Jim Thome.'

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.

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.

NOTES: Royals 1B Eric Hosmer made a terrific, over-the-shoulder catch of a foul popup by Danny Valencia in the seventh inning. ... The Royals have dropped 15 of their last 19 games against the AL Central. ... Kansas City's Billy Butler hit his 22nd double of the year in the seventh inning. His 118 doubles since 2009 are the most in the major leagues during that span.

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Jon Krawczynski can be reached at http://www.twitter.com/APkrawczynski