OAKLAND, CALIF. ? Eric Byrnes keeps earning a spot in the lineup with big hits.

Byrnes singled in the winning run in the 10th inning, and the Oakland Athletics completed their second three-game sweep of the Kansas City Royals in a week, 3-2 Sunday.

Arthur Rhodes (1-1) struck out two in the 10th for the win. Byrnes hit a blooper down the right-field line against Nate Field (2-1) to score Bobby Crosby.

“I didn’t care where I hit it, I just tried to put it in play and make something happen,” Byrnes said. “In that situation, that’s all you can do.”

Crosby reached on a fielder’s choice, then made a gutsy steal of second, just beating the tag by shortstop Angel Berroa. Mark McLemore was intentionally walked to bring up Byrnes.

When asked what pitch he saw, Byrnes smiled and said, “A white ball coming at me.”

In Oakland’s season opener last month, Byrnes had a pinch-hit, two-run double with two outs in the eighth inning of a 5-4 victory over Texas.

The A’s have won a season-high five straight and eight of nine. They’ve beaten the Royals 10 straight times, their longest streak ever against Kansas City.

Oakland won 5-4 in 11 innings Saturday.

Mike Sweeney hit a solo home run for the Royals, who lost their fourth straight and have the worst record in the majors at 13-28. Oakland has outscored Kansas City 30-11 this season.

Oakland's Eric Byrnes, right, is congratulated by teammate Damian Miller, left, after Byrnes drove in the winning run in the Athletics' 3-2, 10-inning victory over Kansas City. With the victory Sunday in Oakland, Calif., the A's completed a three-game sweep of the Royals.

“It rips your heart out,” Sweeney said. “After yesterday, you don’t think you can have a tougher loss than that, then this happens 24 hours later.”

A’s manager Ken Macha is conservative about giving his players the green light to steal — following in the organization’s mantra of taking chances only when there’s a high probability of success.

Crosby beat out a double play to get aboard in the 10th. When he stole second, umpire Mike Everett almost signaled an out but quickly gave the safe sign.

“He gave it to me,” Crosby said of receiving Macha’s permission to run. “I was pumped. I would have lost it if he called me out, to be honest. Berroa was starting to say I was off the bag. I was definitely safe. It was close.”

Berroa, last season’s AL Rookie of the Year, hit an RBI double in the fifth to tie it at 2 and doubled again in the seventh.

Royals starter Dennys Reyes held the A’s in check aside from two early unearned runs, allowing Oakland only five hits through six innings.

Rich Harden retired 10 of the first 11 Kansas City batters, including five on strikeouts, before Sweeney connected for his seventh homer of the year on the first pitch he saw in the fourth.

Kansas City's Wilton Guerrero, left, dives for home plate behind Oakland catcher Damian Miller. The A's beat the Royas, 3-2 in 10 innings, Sunday in Oakland, Calif.

Harden was the losing pitcher in Oakland’s 5-1 loss last Tuesday to Detroit despite a solid outing.

The right-hander worked ahead in the count for much of the afternoon Sunday but had his second no-decision in two career starts against the Royals. He finished with six strikeouts in six innings and gave up two runs on eight hits.

Harden worked out of a bases-loaded jam in the sixth. Matt Stairs singled, Ken Harvey doubled and Desi Relaford was intentionally walked. But Benito Santiago hit a shallow fly to right for the second out and Brandon Berger flied to left.

Kansas City committed two costly errors in the second to give the A’s the lead. Second baseman Wilton Guerrero missed a routine catch on a potential double-play ball that allowed Bobby Kielty to reach first. Then, with Kielty off the bag, Reyes made a wild throw on a pickoff attempt and threw his arms in the air in disgust.

“There’s no room for error,” Kansas City manager Tony Pena said. “Every time we make an error or do something wrong, we pay for it. Today, right away. … It’s the way things are going now.”

Notes: Eric Karros’ seventh-inning double for Oakland was his second hit in his last 17 at-bats. … The A’s are 35-10 against the Royals since 2000. … Both teams are off Monday. The Royals return home, while the A’s head to Boston and Cleveland. … More fans (33,476) attended Sunday’s game on Reggie Jackson bobblehead day than did for Saturday’s game (26,081), when Jackson was in the stadium to have his No. 9 retired. … A’s 3B Eric Chavez got his first day off this season. … The A’s swept the Royals in a three-game set at home for the first time since May 25-27, 1999. … When asked about the A’s, Pena offered this: “The difficulty with the A’s? We’re having difficulty with everybody.”