Billy Butler finished 3-for-4 with two home run ninth inning to 6, in the first of three between the clubs.
"Since this unit's been intact it's been good," Butler said of Kansas City's offense. "We're all feeding off each other and driving balls, putting up runs."
Greg Holland (4-1) worked a scoreless eighth for the win. Felipe Paulino started, but was pulled after 4 1/3 innings after allowing four hits and six runs with four walks.
Scott Sizemore clubbed a three-run homer for the Athletics, who saw their four-game win streak halted.
Bailey got in trouble immediately as Salvador Perez singled, then after a fly out, Alex Gordon bounced a double off the wall in right to score pinch-runner Chris Getz to put the Royals on top, 7-6. Melky Cabrera laced a single to left and Gordon came in for a two-run margin.
Neil Wagner then walked Butler and served up an RBI double from Hosmer to make it 9-6, and after Francoeur fanned, Moustakas drove in two more with a base hit but ended the inninggetting thrown out trying to reach second.
Joakim Soria struck out the side in the ninth to lock up the victory.
The Royals dented Harden for three runs in the opening frame thanks to Hosmer's RBI double and a two-run single by Francoeur.
"It was an odd first inning," Harden commented. "It's not usually what happens to me."
Oakland countered with four in the second on Kurt Suzuki's RBI single and a three-run blast from Sizemore that bounced over the wall in center.
It was the second time in five September games that Kansas City cracked double digits, after the Royals hadn't scored more than 10 in a game since July 29...Oakland hadn't surrendered 10 or more runs in a contest since a 22-9 drubbing against the Yankees on August 25...Butler posted his second multi- homer game this season, after going deep twice on July 29 at Cleveland.