ATLANTA -- Troy Glaus figures it was his turn for some late-game heroics.
"Once I got to two strikes, I tried to do anything I could to get on," Glaus said. "It probably helped. It probably shortened up my swing a little bit to catch up to it."
Brian McCann also homered for the Braves, who have won 13 of 14 at home to improve to 23-7 at Turner Field. Atlanta moved 1½ games ahead of the second-place New York Mets in the NL East.
Glaus' 14th homer came off Robinson Tejeda (2-3) and gave the Braves 13 victories in their final at-bat. Though Glaus leads the NL with 55 RBI, Atlanta had yet to win on his last swing of the game.
"Every win is nice," Glaus said. "You'd like to not save them 'til the ninth inning."
Billy Wagner (5-0) pitched a scoreless ninth to earn the win.
Royals starter Zack Greinke fell behind 2-0 in the first. Chipper Jones hit an RBI single, moved to second on the throw and advanced to third on a passed ball. He scored on shortstop Yuniesky Betancourt's throwing error.
McCann's seventh homer, a leadoff shot in the fourth, made it 3-0.
Kansas City cut the lead to 3-2 in the fifth on Scott Podsednik's sacrifice fly and Jason Kendall's RBI groundout.
The Braves went ahead 4-2 in the sixth when Jason Heyward scored from second on Glaus' grounder. Betancourt tried to begin a double play, but Jones, who was running from first, slid hard enough to knock second baseman Mike Aviles backward onto the ground.
Seeing Aviles was getting up slowly with the ball, Heyward dashed for the plate and scored with a headfirst slide.
"I saw Chip go in hard, and [Aviles] fell down," Heyward said. "So that's when I put my head down and ran."
Eric O'Flaherty replaced Atlanta starter Kris Medlen with one out in the seventh and runners on second and third, but the Royals tied it 4-all on Podsednik's RBI groundout and Kendall's RBI single.
Greinke, last year's AL Cy Young Award winner, allowed six hits, four runs -- three earned -- and no walks in seven innings. The right-hander, who struck out five, was making his first career appearance against Atlanta.
"The pitch to McCann was really bad, but that was the only one I could complain about," Greinke said. "My location was looking good. I kept the ball down really well."
In nine road starts this season, Greinke is 1-5 despite a 3.39 ERA. He was coming off a complete-game victory last Sunday at Cincinnati in which he struck out 12, walked none and ended a four-start losing streak during which the Royals' offense went scoreless for 22 straight innings.
"I thought we played good," Greinke said. "I thought they played good. It was a well-played game all around."
Medlen, who was 3-0 in his last four starts, allowed five hits, three runs and two walks in 6 1/3 innings. The right-hander struck out five.
Jonny Venters pitched the eighth for Atlanta, striking out Betancourt with a runner at third.
Royals manager Ned Yost, whose bullpen had a 0.95 ERA over its previous 28 1/3 innings, credited Glaus for his big swing against Tejeda.
"He hit a 95 mph pitch into the seats," Yost said. "Those things happen."
Medlen has made seven consecutive starts in place of RHP Jair Jurrjens, who has missed 47 games with a strained left hamstring. On Saturday at Triple-A Gwinnett, Jurrjens allowed two runs and eight hits in 4 1/3 innings. He walked one and struck out four. ... Atlanta RHP Takashi Saito (strained left hamstring) will pitch the first inning in a rehab appearance Sunday at Gwinnett. ... Kansas City CF Rick Ankiel had a setback during his minor league rehab assignment and returned to Kansas City for treatment on his right quadriceps.