The Brewers fell to 0-5 and have committed an error in every game.
Brett Eibner, Whit Merrifield and Raul Mondesi Jr., delivered RBIs for the Royals in the sixth, who got their earlier runs from third baseman Mike Moustakas. The lefty-hitting Moustakas logged eight RBIs against left-handed pitchers all last season, but he picked up a pair with a two-run double against Brewers bullpen hopeful Neal Cotts, a veteran southpaw off to a rough start with his new team. Including Monday's two-run, three-hit outing, Cotts has been charged with three earned runs on four hits and three walks in 1 1/3 innings.
Cotts pitched in relief of starter Jimmy Nelson, who surrendered only one harmless two-out hit over two otherwise spotless innings in his first outing this spring.
"I felt pretty good out there," said Nelson, whose debut had been delayed by a left hamstring tweak. "I was able to work on some things that were good to work on in game situations. I think I was just a tick up in the strike zone, but that's an easy adjustment."
Royals starter Jason Vargas allowed a run on two hits in two innings, with three strikeouts. One of those strike threes got past the catcher for a wild pitch, allowing Brewers left fielder Khris Davis to reach safely. Martin Maldonado followed with an RBI triple that gave the Brewers a 1-0 lead.
"Left a couple fastballs up that they were able to put some good swings on," Vargas said, "and for the most part I was able to throw the changeup down in the zone and get some good results."
Milwaukee manufactured another run in the third inning against Royals reliever Kelvin Herrera, when Logan Schafer walked, stole two bases and scored on a Jean Segura groundout. Outfielder Matt Long homered for the Brewers in the sixth.
Up next: After three road games in four days, the Royals will return to Surprise Stadium on Tuesday to take on the AL Central-rival White Sox at 3:05 p.m. CT. Jeremy Guthrie will make his Cactus League debut, with Brandon Finnegan, Greg Holland, Jason Frasor, Casey Coleman, Louis Coleman and Scott Alexander expected to follow. The game will be aired on KCSP AM-610 and MLB.com.
Adam McCalvy is a reporter for MLB.com. Read his blog, Brew Beat, and follow him on Twitter at @AdamMcCalvy. This story was not subject to the approval of Major League Baseball or its clubs.