KANSAS CITY -- Mason Miller had a tough act to follow on Sunday after pitching seven hitless innings in his previous start. But Miller was up to the task and impressive once again.

The A’s right-hander continued to build his early-season resume by limiting the Royals to just two runs on five hits through six innings. Miller didn’t get much offensive support and the A’s wound up taking a 5-1 loss at Kauffman Stadium. But the arrows are pointing up for Miller as he reflects on his four starts in the Major Leagues.

Five days after holding the Mariners hitless through seven, Miller improved in one important category. He allowed four walks against Seattle, but only one in his follow-up against the Royals.

“I was happy that I kept the walks down,” Miller said.

In retrospect, Miller had only two real glitches, but that cost him in a tight, low-scoring game in which Kansas City was up 2-1 through seven innings. In the first inning, Miller started Salvador Perez with a slider, but then came with five straight four-seam fastballs. Perez hit the last one for a 462-foot homer to left-center on a pitch that registered 99.9 mph.

“Probably could have mixed it up a little more,” Miller said. “... I was trying to go down and away. I think where I went with it [was] middle-up. That’s his spot.”

The only other run off Miller came on two singles, sandwiched around a wild pitch. That wild pitch was the big item in the equation because it put the lead run in scoring position in a 1-1 game.

“[The wild pitch] is something I can control,” Miller said.

Oakland manager Mark Kotsay was pleased with Miller’s reduction in walks from his previous start and how he was able to get through six innings, which allowed several high-leverage relievers to get a day off following a couple of stressful bullpen days.

“The kid is building momentum,” Kotsay said. “Overall, a good performance. He continues to go in the right direction.”

The A’s could only tip their caps to Perez in the series finale after Oakland took the first two games of the weekend set for its first series win of the season. Besides his mammoth home run and 3-for-4 day at the plate with three runs scored, Perez threw out Esteury Ruiz trying to steal second after Ruiz led off the sixth with a single. Ruiz had been 16-for-17 in steal attempts when Perez made a perfect and forceful throw to eliminate a potential Oakland rally.

“It was a great game for Salvy,” Kotsay said. "I told our pitching coach that it wouldn’t be a trip to Kansas City if Salvy didn’t hit a homer. That’s the type of player he is.”

The A’s couldn’t get much going against Royals starter Ryan Yarbrough. Even after a scary sequence in the sixth when Yarbrough took a shot to the face on Ryan Noda’s liner and had to leave the game, Oakland remained quiet against the Kansas City bullpen.

A sweep would have been extra nice for the A’s, but they headed on to New York feeling they were turning a corner after taking two of three from the Royals.

“We like the way we have played the last couple of weeks,” left fielder Brent Rooker said. “We’ve really battled, but had some things not go our way when we had a chance to win. To take this series, that’s huge.”