CHICAGO — His second season has been a struggle for Braves right fielder Jason Heyward, but Cubs fans might find that hard to believe.

Heyward hit a fourth-inning grand slam, the first of his career, and the Braves hung on to beat the Cubs 5-4 on Tuesday night at Wrigley Field, pushing their winning streak to six games and their record to a season-high 26 games over .500.

Braves closer Craig Kimbrel pitched a scoreless ninth for his 40th save to tie the major league rookie record set last season by Neftali Feliz of Texas. Kimbrel leads the majors in saves and has a streak of 31 2/3 scoreless innings over 32 appearances since June 11.

Rookie phenoms from this season and last (Heyward) helped the Braves match their season-high winning streak.

“I’m not thinking about a record or streak, I’m just trying to help us win," said Kimbrel, who struck out Tyler Colvin with a runner at second base to end the game.

Heyward has been benched some recently and hit under .200 since May 1 before Tuesday, when he was 3-for-4 and matched a career-high with four RBIs. He's been working on trying to hit the ball to the opposite field, and that's where his slam went out -- to left-center field.

"I wasn’t exactly sure when it was going to show up, but tonight’s definitely a good start for that," said Heyward, who is 9-for-16 with three home runs and eight RBIs in his career at Wrigley.

He's had four RBIs four times in his career, and three of those games have come against the Cubs, including each of his past two starts in Chicago.

Coincidentally, both of those were starts by Braves rookie pitcher Mike Minor, who won Tuesday despite blowing most of a 5-0 lead when he gave up four runs (three earned) in the fifth inning.

On Aug. 22, 2010, Heyward went 4-for-4 with two homers and four RBIs against the Cubs, and Minor struck out 12 in six innings to win his third major league start.

A year and a day later, Heyward was in the lineup because hot-hitting rookie Jose Constanza sprained an ankle in Monday’s series opener. Heyward had hit .197 with five homers and 17 RBIs in 70 games since May 1, but Tuesday he reminded everyone what a force he can be.

“Good for him, for his psyche and his confidence," Braves manager Fredi Gonzalez said. "Good time to come out swinging. First grand slam of his career."

Heyward's two-out slam off Casey Coleman (2-6) landed in the left-center bleachers and capped a five-run inning that staked Minor to a 5-0 lead. In the Braves dugout, Chipper Jones was pleased. He's worked some recently with Heyward, trying to get him to hit to the opposite field.

“That’s what he’s got to do," said Jones, who also had three hits to raise his average to .282. "His first at-bat he things pull first. He finally said, you know what, I’m going to stay of everything, go the other way. And what do you know, something good happens.”

Heyward said, “It’s not easy when you’re not playing every day. But I understand the situation we have at hand. I want to win games. I want to go to the playoffs and I want to experience that again. We want to go as far as possible.

"I definitely understand I’m not going to be in there every day. I’ve just got to make the most of it.”

Minor (4-2) was replaced after giving up four runs (three earned) in the fifth. Alfonso Soriano led off the inning with a homer that ended a 30-inning scoreless streak by Braves pitchers. The wind was blowing straight out to center field, conditions ripe for hitting at Wrigley.

“After we got the five runs, I just wanted to go after hitters and throw strikes," Minor said. "I caught the middle of the plate against Soriano, and after that it kind of snowballed on me. I hit the next batter, I was missing spots, it just wasn’t a good inning. I couldn’t get it going.”

Nevertheless, Minor improved to 4-0 in his past five starts. He was charged with four runs (three earned) and six hits with six strikeouts, and has 18 strikeouts in 11 career innings at Wrigley.

The Braves had two out and none on in the fourth before mounting their rally against Coleman, who is winless with a 10.80 ERA in his past six games.

Dan Uggla’s infield hit started the rally, and Jones followed with a single. Eric Hinske walked to load the bases and bring up Alex Gonzalez, who had been 5-for-50 with two walks with runners in scoring position and two outs.

This time he showed some patience, getting ahead in the count 3-1 before taking a close full-count pitch for an RBI walk and 1-0 lead.

Heyward, batting eighth behind Gonzalez, cleared the bases with a homer on a 1-2 curveball. It was his fourth home run in his 29th career at-bat against the Cubs.

After Soriano’s homer, Aramis Ramirez added a two-out, two-run double, and the Cubs tacked on an unearned run in the inning when Alex Gonzalez bounced a throw that backup first baseman Eric Hinske couldn’t field cleanly.

Ramirez set a career high with five hits and is 8-for-9 in the first two games of the four-game series. He hit a two-out bloop single off Kimbrel in the ninth and went to second on Heyward's error on the play, before Kimbrel struck out Tyler Colvin to end the game.

Kimbrel is perfect in 22 save opportunities during his 31-2/3-inning scoreless streak, which is 2-1/3 innings shy of the longest streak in the majors this season, by Philadelphia starter Cliff Lee.

“I’ll look back on it at the end of the year," Kimbrel said. "Right now I’m just worried about helping us win and helping us get to the playoffs and through the playoffs."