Robinson Cano, making his first appearance since Wednesday after he had root-canal surgery, went 3-for-3 with three singles for the Mariners.
"It feels good at the plate, and I'm not trying to do too much," Cano said.
Billy Butler had a double and scored from first after a single to lead the Royals' offensive attack. Catcher Salvador Perez left the game after just two innings with a contusion on his left palm; X-rays were negative.
Shields allowed an unearned run in the first inning but retired the side in order the next two innings. After picking off Cano at third base, Shields allowed a second run in the fourth on a James Jones single that drove home Justin Smoak.
For the day, Shields allowed two runs (one earned) on five hits while striking out five and walking none.
"It went pretty smooth," Shields said. "I mixed in a couple of curveballs, which is the first time in Spring Training. I actually didn't think I was going to throw it today. But it felt pretty decent in the 'pen, so I threw a few. I came out of my delivery a few times, but overall it went pretty well."
The Royals tied the game in the second inning when Butler scored on a Mike Moustakas single off Maurer, and they broke it open in the third with all five runs scoring with two outs.
Gordon's double off Minor League reliever Stephen Shackleford was followed by three walks and a Moustakas single, his second RBI of the day and team-leading 12th of the spring.
Up next for Mariners: The Mariners' other split-squad game of the day has them facing the D-backs on Monday at 7:10 p.m. PT on Gameday Audio. Then on Tuesday, less than three weeks from their Opening Day meeting against the Angels, the Mariners will take on their AL West rivals for the second time this spring in a 1:05 p.m. PT start Tuesday at Tempe Diablo Stadium on MLB.TV. Scott Baker, who returned from Tommy John surgery last September and was signed to a Minor League deal by the Mariners this past winter, enters his third start of the spring sporting a 1.80 ERA, having allowed one earned run on four hits through his first five innings of work in Cactus League play. Baker, a 15-game winner with the Twins in 2009, will meet Angels lefty starter C.J. Wilson.
John Schlegel is a national reporter for MLB.com. You can follow him on Twitter at @JohnSchlegelMLB. This story was not subject to the approval of Major League Baseball or its clubs.