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 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 Royals: Left-hander Jason Vargas will try to extend his scoreless streak as he makes his third start for the Royals in a 3:05 p.m. CT game against the Dodgers on Tuesday at Surprise Stadium on MLB.TV. Vargas has not given up a run in five innings despite allowing a combined six hits. Right-hander Dan Haren will start for the Dodgers. It marks the Royals' third game in which instant replay will be available. There were three challenges by the Brewers on Saturday, but all three calls were upheld. Also on Tuesday's schedule is a "B" game against the Rangers at 9:30 a.m. MT at the Surprise complex. Everett Teaford, Kelvin Herrera and Tim Collins are scheduled to pitch for the Royals. Matt Harrison is on the Rangers' list.
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.