Jordan Pacheco and Nolan Arenado each singled, and after an out, Yorvit Torrealba singled to left field. Alex Gordon launched a throw high above catcher Salvador Perez and two runs scored on the play. DJ LeMahieu singled home the third run.
Guthrie gave up a fourth run in the sixth inning on two-out singles by Michael Cuddyer, Pacheco and Arenado. Pacheco was thrown out trying to score, ending the inning.
The Rockies tacked on three insurance runs in the ninth, two of them coming on a bases-loaded double by Corey Dickerson.
Mike Moustakas' home run to right field off Rockies starter Juan Nicasio gave the Royals a 1-0 lead in the second inning. That was the only damage to Nicasio in his five innings.
Nicasio, a hard thrower who is trying to diversify his pitching plan, threw fastballs reaching 97 mph -- Eric Hosmer was the victim of two blazing strikeouts -- but he also used his developing changeup.
"I was working like it was in the season -- keeping my fastball down, throwing a lot of changeups and sliders down," Nicasio said. "It was like a normal game."
Moustakas also singled and raised his average to .426 (20-for-47), so he's happy with his batting stroke at this point.
"I've been working on it all offseason, getting back to how I used to hit, and I'm trying to get more comfortable in the box and I feel like I've gotten to that point," Moustakas said. "So I'll just kind of stay here and keep going from where we're at."
Royals up next: Right-hander Wade Davis gets back into Cactus League action for the first time since March 3. He missed a turn because of shoulder soreness, and his return came in a Minor League game. It will be just his third official start for the Royals when he faces the Dodgers at 3:05 p.m. CT on Wednesday at Surprise Stadium. J.C. Gutierrez, Tim Collins, Donnie Joseph and Louis Coleman are scheduled to come out of the bullpen.
Dick Kaegel is a reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.