Mark Trumbo, strengthening his candidacy for the Angels' 25-man roster, slammed a tremendous two-run homer to left-center in the second inning against Royals starter Kyle Davies.
Torii Hunter and Howard Kendrick delivered two hits apiece for the Angels.
Facing Angels starter Ervin Santana, Maier singled through the middle in the first inning after Melky Cabrera had walked and stolen second. Kila Ka'aihue singled home Maier, who'd stolen second.
Maier, serving as designated hitter, singled home another run during a two-run sixth. He singled and stole his second base in the eighth, scoring when center fielder Travis Witherspoon robbed Clint Robinson of a hit on a sacrifice fly. Maier is 7-for-11 this spring with four RBIs.
Santana got an out in the second before departing, having reached his pitch count. Davies made it through two innings, giving up the two runs on Trumbo's blast following Kendrick's first of two singles. It was Trumbo's second homer of the spring, and he leads the team with four RBIs.
"I was happy with it," Davies said. "I commanded my delivery pretty good, commanded the baseball fairly good. There were a couple of pitches that got away and one of them got hit, but overall my command of the fastball was pretty good. Command of the curveball and changeup was really good."
Joakim Soria worked a scoreless third inning, turning things over to Nate Adcock. Tim Collins pitched out of a bases-loaded jam in the sixth, retiring Hank Conger.
Romack's first homer of the spring, a drive to left, came against southpaw Trevor Reckling. Fernando Rodney escaped a bases-loaded predicament in the third inning. Garrett Richards, a premium right-handed prospect, allowed three earned runs in 2 1/3 innings.
The Royals are 4-1 in Cactus League play, while the Angels fell to 3-3.
Up next for Angels: Encouraged by his first start of the spring against the Dodgers despite giving up three runs on five hits in two innings, Scott Kazmir will try to stretch it another inning on Friday against the White Sox at Tempe Diablo Stadium. He'll face former NL Cy Young Award winner Jake Peavy, also on the comeback trail, in a 12:05 p.m. PT Cactus League encounter. First baseman Mark Trumbo will continue to make his case for a role on the 25-man roster with his booming power at first base.
Up next for Royals: After two road games, the Royals return to Surprise Stadium at 2:05 p.m. CT on Friday to meet the Chicago Cubs, who usually spark an upsurge in attendance. Left-hander Bruce Chen, who worked two scoreless innings in the Cactus League opener, will make his first start as he tries to secure a place in the rotation. Young lefties Danny Duffy and Blaine Hardy, who had bumpy goings in their debuts, are also scheduled to work against the Cubs. Billy Butler, who led the club with five RBIs in the first four games, is likely to return after a day off.
Lyle Spencer is a reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.