Haren yielded seven singles, walked one and struck out one.
"I gave up seven hits. I think they were all singles," Haren said. "For the most part, a lot of ground balls which is always a good thing for me. It means I'm keeping it down in the zone.
"At the beginning of last year, I was haunted by the home run, just leaving too many balls up out over the plate," he said. "The second half was keeping the ball down and getting more results like today, a lot of groundball outs."
The Dodgers leave Arizona after their game Sunday for two regular season games in Sydney, Australia. Haren said he has yet to get a "definitive answer" on whether he would make the trip. Clayton Kershaw and Hyun-Jin Ryu are the scheduled starters against the Arizona Diamondbacks.
"If I had to do it, I would do it," Haren said. "I told them I would have no problem doing it. If I'm not going to throw there and I could stay back I think that's better for everybody really."
Noel Cuevas hit a three-run homer in the ninth and Scott Van Slyke a two-run drive in the eighth.
Justin Maxwell went 3 for 5 for the Royals, including a two-run single in the eighth.
Royals left-hander Jason Vargas allowed a run on four hits in four innings, the first run off him in nine innings over three starts.
The Dodgers loaded the bases in the fourth off Vargas, but came away empty when A.J. Ellis hit a flyball to center field to end the threat.
Dodgers: Haren threw 65 pitches, 39 for strikes, before departing.
"I got through four. I could have gone five," Haren said. "I'm ahead where I need to be really. I'm a little tired. I don't know if it's a dead arm or something like that. I've thrown a lot so far for being March 11."
Royals: Vargas, who will start the second game of the season, gave up a run on four hits, a walk and a hit batter, while striking out two in four innings.
"That last inning I was able to work out of a jam, which is always nice to be able to do," Vargas said. "I guess I don't really have any certain point of where I want to be (this time in spring training) rather than being able to throw the pitches I need to and the count and situations they need to be executed in. So far, so good."
Dodgers: Zack Greinke, who has faced only one batter in spring training because of a calf injury, took part in fielding drills Tuesday. If he has no discomfort Wednesday, he is scheduled to pitch two innings against the Diamondbacks.
Royals: All-Star catcher Salvador Perez has a bruised left palm from a foul tip Monday against the Mariners, leaving in the third inning. A fluoroscope test and X-ray were negative. Perez sat out Tuesday, but manager Ned Yost said there is "a 97 percent chance" he would play Wednesday.
Shortstop Alcides Escobar was a late scratch with stiffness in his right throwing shoulder.
"It's just a little nagging thing," Yost said. "It's not a major issue."
Royals third baseman Mike Moustakas, who is batting .435 with a .913 slugging percentage, went 2 for 3 in a B-game Tuesday against the Rangers.
NO BLUE FOR RED
The Dodgers assigned right-hander Red Patterson to minor league camp. Patterson was 7-4 with a 3.03 ERA in 2013 with Triple-A Albuquerque, striking out 109 in 107 innings. He was 0-1 with a 1.42 ERA in three exhibition games.