"You can't put enough ground between yourself and the other teams," Wagner said. "We've got to continue to battle and get the lead as far as we can get it because there's going to be a time where we hit a tough spell and there's going to be a time when they're hot."
Melky Cabrera added an RBI single in the eighth off Blake Wood (0-1) for the Braves, who improved to 24-7 at home. Atlanta moved 2½ games ahead of the second-place New York Mets in the NL East. Two-time defending NL champion Philadelphia is in third place, 5½ games back.
Craig Kimbrel (2-0) earned the win by pitching a scoreless eighth, but it wasn't easy. The right-hander loaded the bases on two walks and his own fielding error before striking out two and escaping the jam on Billy Butler's popup.
"I kind of put myself in a tough situation there," Kimbrel said, "but we got back in there and were able to get three outs."
Wagner struck out two in a scoreless ninth for his 14th save in 16 chances. After earning his 399th career save, he pulled aside Kimbrel to give the rookie some advice.
"I'm trying to tell him you cannot create your own save, especially in a tie game," Wagner said with a laugh. "But he just ain't getting it yet. As long as you get out of that, the kid's on the right track. The kid's head and shoulders above where I was at that age."
The Royals rallied for a 5-4 lead with RBI singles in the second by Brayan Pena and Chris Getz, and with a three-run third that included Jose Guillen's RBI single, Mitch Maier's run-scoring infield single and Getz's RBI double.
Failing to score in the eighth, though, soon left Kansas City with a third straight loss.
"We had the bases loaded and nobody out in the eighth, but we couldn't get anything out of it," Butler said. "We just didn't come through today. Obviously, they are playing really well."
Kenshin Kawakami, the first starting pitcher in Braves history to begin a season by losing nine straight decisions, was chased by Guillen's hit in the third, the last of three consecutive singles to begin the inning.
Kawakami allowed six hits and five runs -- four earned -- with no walks and one strikeout. It was the shortest of his 39 starts in the major leagues. He also has committed three errors in his last two games.
Asked if he thinks a move to the bullpen would help him work through some of his trouble with mechanics, Kawakami wasn't sure.
"I haven't really thought about it much," he said through a translator. "But being a starter, I'm not really doing my job right now. I'm ready for whatever might be coming to me."
Royals starter Kyle Davies walked a career-high seven in 4 1/3 innings. The right-hander gave up four hits and four runs while striking out six. In his last five starts, Davies is 1-2 with a 9.78 ERA.
Pitching in his hometown and making his first appearance against the team that traded him to Kansas City in 2007, Davies insisted nerves didn't derail him.
"When I picked up the tempo a little bit, the game got a little better," he said. "But in the fifth, I lost command again. I wasn't amped up. I just struggled with my command."
Braves RHP Takashi Saito could come off the 15-day disabled list before Tuesday's road game against the Chicago White Sox. Saito struck out one in one inning of a rehab appearance Sunday at Triple-A Gwinnett. ... Royals manager Ned Yost said RHP Gil Meche has "moved out of recovery phase" with a bullpen session. Meche, on the DL with shoulder bursitis, is 0-4 with a 6.66 ERA in nine starts. Kansas City hopes he can return next month.