Hosmer, who hiked his batting average to .353, doubled in the fourth and scored on Rios' single. Rios also doubled in the sixth and scored on Salvador Perez's single. Moustakas had an RBI double in the sixth.
"We swung the bats good," Royals manager Ned Yost said. "Hos had some good at-bats. It was a good day."
It was the first time the clubs had met since Game 7 of the World Series, which the Giants won 3-2.
"The atmosphere was a little less than the last time we played these guys," Yost said, "but it's still fun."
Giants left fielder Nori Aoki, who played for the Royals last season, singled, doubled and walked against his former teammates. It was his second straight multihit game.
"Before the game, I went to the Royals' bench and said hello to the manager, coaches and everyone," Aoki said through an interpreter. "It reminded me of my Royals days."
Both of Aoki's hits were off Royals left-hander Danny Duffy.
"I wanted to face a left-handed pitcher," Aoki said. "Last year, I watched Duffy from right field and I had a good image of Duffy."
Duffy went 5 1/3 innings, the longest outing by a Royals starter this season, allowing two runs on six hits.
Brandon Crawford also had two hits, including an RBI double.
FINNEGAN TO MINORS
The Royals optioned Brandon Finnegan, who became the first player to play in the College World Series and the World Series the same year, to Double-A Northwest Arkansas on Sunday.
The Royals' first-round pick out of TCU last year, will be used as a starter in the minors after pitching out of the Kansas City bullpen last September and in the postseason.
Giants: RHP Chris Heston, who was optioned Friday to Triple-A Sacramento, had an impressive three scoreless innings, allowing one hit and striking out five against a Royals' lineup that included eight regulars.
Royals: Duffy's pitch count reached 72 before he was pulled after Crawford's double. "I felt like I was locating pretty well," Duffy said. "In the sixth, I felt I made a couple of good pitches and fell behind Crawford. That was the only pitch I wish I could have back. Overall, I felt pretty good."
Giants: RHP Eric Cordier, who has not pitched since March 8 because of a forearm strain, is scheduled to resume a throwing program this week.
Royals: Eibner, who exited the game Saturday with a bruised left foot, said he was OK on Sunday before he was assigned to the minor league camp. "I just fouled a two-seam off the top of my foot, caught it flush," Eibner said. "Running to first, I didn't have much feeling in it. I don't think I gave myself enough time to get some blood flowing through there. I kind of rushed back in the box. I felt just really uncomfortable."
BOCHY SOLID AGAIN
RHP Brett Bochy pitched a scoreless eighth, allowing one hit, to lower his ERA to 1.50 over seven appearances. Giants manager Bruce Bochy is his father.
Giants: RHP Jake Peavy, who was 0-2 with a 12.79 ERA in two World Series starts last October against Kansas City, will face the Royals on Monday at Scottsdale.
Royals: Omar Infante, who has been limited to DH duties because of a tender right elbow, played second base in a minor league game Sunday. If all goes well, Infante will make his Cactus League debut at second Monday.