Cuevas hit Coleman's 2-1 pitch high over the left-center-field wall. The Dodgers loaded the bases before Coleman finally ended the inning without more scoring.
Justin Maxwell's two-run single had given the Royals a 5-4 lead in the eighth inning. Maxwell, who was 3-for-5 as the designated hitter, delivered off right-hander Javy Guerra. His single to left scored Johnny Giavotella and Jimmy Paredes, who had advanced into scored position on a passed ball.
Scott Van Slyke had a two-run homer for the Dodgers in the top of the eighth, his second homer in a week.
The win gave the Dodgers a 5-6-4 record; the Royals are 6-6-1.
Royals left-hander Jason Vargas ran his scoreless streak to seven innings with perfect pitching in the first and second. However, he started the third by hitting Justin Turner with a pitch, two outs later, he scored on Chone Figgins' single. But when Figgins tried to score from second on Carl Crawford's hit, he was thrown out by Gold Glove-winning left fielder Alex Gordon.
Vargas pitched out of a bases-loaded jam in the fourth, his final inning. His ERA stands at 1.00 after three appearances.
Dodgers starter Dan Haren also worked four innings and gave up one run. That came in the fourth after the Royals loaded the bases with no outs on singles by Maxwell and Danny Valencia and a walk to Lorenzo Cain. Only Maxwell scored, however, sprinting home after shortstop Figgins caught Brett Hayes' popup in short left field.
Haren allowed seven hits and one walk. He's permitted two runs in 10 innings for a 1.80 ERA this spring.
"I gave up a few hits, but I think they were all singles," Haren said. "I was keeping the ball on the ground, for the most part, which is really good. I worked out of a few jams. I feel good."
The Royals snapped the 1-1 tie in the sixth inning against veteran Jamey Wright. An error, a walk and a hit batter loaded the bases with one out and Carlos Peguero drilled a two-run single up the middle. But Wright escaped further damage.
Wade Davis, recently assigned to the Royals' bullpen, gave up a run in the seventh. A.J. Ellis, who opened the inning with a walk, scored on a wild pitch.
The Royals loaded the bases in the seventh with no outs against left-hander Paco Rodriguez but failed to score.
After Royals lefty Scott Alexander began the eighth with a walk to Aaron Bates, Van Slyke pounded a homer to center field to give the Dodgers a 4-3 lead.
Up next: Zack Greinke, who is recovering from a strained right calf, took part in pitchers fielding practice and other drills Tuesday morning at Camelback Ranch. If all goes well, the Dodgers right-hander will start Wednesday's Cactus League game against the D-backs, available live on MLB.TV at 1:05 p.m. PT.
Zach Lee will start if Mattingly decides to hold Greinke back.