Kimbrel suffered his second blown save in 11 chances, but the Braves bailed him out in the 10th.
Braves manager Fredi Gonzalez said Renteria faced a tough decision in walking Upton to face Freeman.
"You've got to pick your poison," Gonzalez said.
Luis Valbuena led off the 10th with a single to right field off Alex Wood (3-5), who then recorded three straight outs in his first relief appearance of the season. The Braves announced before the game that Wood was moving to the bullpen for one week.
The Braves earned only their second win in their last 10 games. The Cubs, last in the NL Central, have lost five of six but took some solace in the ninth-inning comeback off Kimbrel.
"All in all, I take away we fought a pretty good battle, but we just fell a little short," Renteria said.
Teheran retired 17 consecutive batters after Olt's homer in the third inning.
Teheran began the night fifth in the majors with a 1.80 ERA and he lowered the mark to 1.71. He had a season-high nine strikeouts with two walks.
The Braves' only runs against Hammel came on a string of three straight two-out hits in the third. Freeman and Evan Gattis singled, Gattis moved to second on a wild pitch and Johnson drove both runners in with a single to left field.
"For a fastball-hitting team like (Atlanta), you've got to be really careful about being down," Hammel said. "In that inning, the ball was running back over the plate and they were able to get the barrel to it."
NOTES: The start of the game was delayed 18 minutes by rain. ... Johnson capped his big night with an eighth-inning single before stealing second — his first stolen base since 2012 and only the 11th of his career. ... Wood had been scheduled to start Sunday against the Cubs. Instead, RHP Aaron Harang will make Sunday's start. Gonzalez said Wood will be back in the rotation on May 17 against St. Louis. ... The series continues Saturday night, when Braves RHP Ervin Santana (3-0) faces Cubs RHP Jeff Samardzija (0-3).
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