Vogt, limited to designated-hitter duties as he continues to rehab a surgically repaired right elbow, accounted for four of Oakland's runs, hitting a solo homer off Royals lefty Sam Selman in the fourth and a three-run shot against right-hander Christian Binford in the fifth.
"Obviously, the results are fun today," Vogt said. "I haven't been feeling great, so to have two swings like that where I actually trust the elbow, trust that everything was going well, it was nice just to take full swings and not have to feel any pain. I'll take that over the home runs, but it's always nice to hit a home run."
A's right-hander Jesse Hahn, who missed the second half of the 2015 season with a forearm strain, took the mound in a game for the first time since July 1 and allowed one hit over two innings, a two-run homer to Moustakas. He walked one but got five ground-ball outs.
A's right-hander Kendall Graveman also made his spring debut, allowing two runs (one earned) in two innings, and relief acquisitions Ryan Madson and John Axford combined for two scoreless innings in their first Cactus League appearances.
Kansas City starter Kyle Zimmer, the club's top pitching prospect, limited the A's to one run on four hits with two strikeouts in three innings. Josh Reddick drove in the lone run off the KC righty, singling home Coco Crisp, who scored from first.
Up next for the Royals: The Royals return to Surprise Stadium on Tuesday to host the Rockies at 2:05 p.m. CT. Edinson Volquez, who could be the club's Opening Day starter, gets the nod. He worked 1 2/3 innings in his first Cactus League outing and gave up two hits and one run.
Up next for the A's: The A's will host the Rangers at Hohokam Stadium on Tuesday afternoon, with lefty Eric Surkamp set to take the mound for a 12:05 PT start. Right-hander Liam Hendriks is also scheduled to pitch in the game, as is righty Ryan Doolittle, the brother of A's closer Sean Doolittle.
Jane Lee is a reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.