Kansas City, Mo. ? The Oakland Athletics are tied for last in the American League in home runs, so it figures that they don’t rely often on the long ball to win games.

Oakland pitcher Vin Mazzaro, left, tags out Kansas City’s Chris Getz at first base during the third inning. The A’s beat the Royals, 9-6, Sunday in Kansas City, Mo.

They did Sunday.

Adam Rosales, Kevin Kouzmanoff and Jack Cust each went deep, and Vin Mazzaro pitched into the eighth inning to help the A’s beat the Kansas City Royals, 9-6, and finish a three-game sweep.

The A’s have won five straight and 12 of 18 to even their record at 46-46, the first time they have been at .500 since June 15. The Royals have lost six straight, one shy of their longest losing streak this season.

“In spring training we talked about when we added Kouz about hitting more home runs,” Cust said. “We’ve got some guys who can do that. We don’t have guys who hit 30 homers, but we’ve got four or five who can hit some and guys who can drive in runs.”

Cust’s three-run homer with two outs in the ninth made it 9-1, but loomed big in the bottom of the inning when the Royals scored five runs.

“Obviously it helped with that thing there at the end,” Cust said.

Cust, who has hit 25 or more home runs each of the past three seasons, homered in back-to-back games in the final two games before the All-Star break.

“I predicted he’d have a solid second half and he appears to be doing that,” Oakland manager Bob Geren said. “A guy like that is going to get going good at some point.”

Rosales, who had the winning hit with two-out in the ninth Saturday, homered in the fourth after Cust walked. Rajai Davis doubled home Landon Powell with the third run of the inning.

Kouzmanoff, who had seven RBIs in the series, homered in the fifth. His sacrifice fly in the seventh scored Coco Crisp, who stole two bases in the inning.

“We did everything right in this series,” Kouzmanoff said. “We’re all feeling pretty good right now and we’re all taking advantage of our opportunities.”

The Royals are going the opposite direction of the A’s, and manager Ned Yost had a closed-door meeting after the loss to address the lack of focus.

“We had a nice little bounce back in the ninth, but if our intensity was a little bit greater in the first eight innings we might have won that game,” Yost said. “That’s all part of it, developing a mindset that nothing matters to you. It doesn’t matter about the heat, about an umpire, who the opposing pitcher is. Your intensity has to be consistent every single day.

“You can’t take an inning off, a pitch off. You can be down 9-1 and end up putting a five or six spot on the board, but it does you no good, because we were flat the first eight innings.”

Mazzaro (5-2) limited the Royals to seven hits — all singles — in a career-high 72?3 innings. He’s worked at least seven innings in four of his past five starts after going 19 consecutive starts without pitching beyond six.

Mazzaro gave up a run in the first when Billy Butler’s two-out single scored Jason Kendall, but nothing after that.

Royals right-hander Brian Bannister (7-8) lost for the first time in five day-game decisions this season. Bannister, who is 0-3 in four starts since a June 23 victory at Washington, tied a career high with six walks, hit a batter and gave up five runs in 61?3 innings.

Chris Getz and Scott Podsednik each drove in a pair of runs in Kansas City’s five-run ninth off four Oakland relievers. Andrew Bailey was summoned for the final out to log his 20th save in 23 opportunities.

“We played terrible,” Royals catcher Jason Kendall said, summing up the series.

Notes: 2B Mike Aviles, who was in a 1-for-16 slide and had just one extra-base and one RBI in his past nine games, was held out of the Royals lineup. Getz replaced him in the lineup. … Oakland swept a three-game series at Kauffman Stadium for the first time since Aug. 5-7, 2005.