Yet the celebration was tempered.
Los Angeles manager Dave Roberts said Kershaw would go on the 10-day disabled list no matter the results.
"I'm not optimistic just because I got taken out of the game," Kershaw said. "At the same time, some of the symptoms aren't as bad as they could be. Hopefully find out more (Sunday evening)."
This is not the first time Kershaw has dealt with a back issue. Last year, he missed 2 1/2 months during the season with a herniated disk that didn't require surgery.
"I don't want to compare because there's so many variables," Kershaw said. "I don't even know how to compare it, honestly."
Kershaw said he felt something different on his final warmup pitch in the second inning.
"It was a little concerning when we saw him grimace on the mound," Forsythe said. "We understand it's not as bad as it was last year. It was a smart move and precautionary to get him out of there and see where it's at after (Sunday)."
Roberts said the injury could be muscular in nature.
The sight of Kershaw leaving a game early is scary for the Dodgers, who lead the National League West by 10 1/2 games and have designs on the franchise's first World Series championship since 1988.
Kershaw struck out two, walked one and didn't allow a hit or a run while throwing 21 pitches before exiting. He is 15-2 with a 2.04 ERA and is having another Cy Young Award-caliber season. Kershaw hasn't lost a start since May 1.
"A lot of frustration," Kershaw said. "Just countless hours of back maintenance and rehab just trying to stay healthy. Felt really, really good up to this point. There's definitely some frustration there, for sure."
The Dodgers (68-31) did what they always seem to do and won for the 46th consecutive time when they had a lead at any point in the game. They split the series with the Braves (47-50), who won the first two games.
Austin Barnes and Cody Bellinger homered for the Dodgers, but Kenley Jansen blew a save for the first time in 25 chances this season. Matt Adams' three-run shot off Jansen with two outs in the ninth forced extra innings.
In the 10th, Atlanta reliever Jim Johnson (6-2) gave up a leadoff single to Chris Taylor, and Corey Seager reached on a fielder's choice. Justin Turner singled Seager to third, and the Braves intentionally walked Bellinger. That gave Forsythe the opportunity, and he delivered.
After Jansen couldn't get the four-out save, Brandon Morrow (3-0) picked up the win with a scoreless 10th.
There are bigger concerns for Los Angeles, namely the health of Kershaw.
"Every time a guy like that goes down, it makes you sick to your stomach," Jansen said. "Man, hopefully everything is all right."
Kershaw uncharacteristically bounced a curveball in the dirt and was visited by a trainer and Roberts during the second inning with Tyler Flowers at bat. He walked Flowers and then struck out Adams to end the inning.
Trainers talked to the lefty in the dugout, and then Kershaw went into the clubhouse. Long reliever Ross Stripling was warming up in the bullpen, and he entered the game after Trayce Thompson pinch-hit for Kershaw in the bottom of the second.
Much later, Adams came through to tie the score.
"It's just fun to be part of a club like this," Adams said. "It shows no matter who is out on the mound, what team we're going up against, we never give up until that last out is recorded. Today was a good example of that."
After the homer, Jansen got Johan Camargo to fly out to center field to end the inning.
The Braves struck first in the game. Brandon Phillips -- who was back in the lineup after missing two games with a hamstring injury -- hit a two-out double to right to give Atlanta a 1-0 lead.
In the fourth inning, Forsythe and Enrique Hernandez walked, and Barnes hit an 0-2 fastball for a three-run homer off rookie Sean Newcomb.
"I was probably more mad about those two walks before the home run," Newcomb said. "On (the) 0-2 (pitch), I executed the pitch I wanted to, he just got to that fastball inside, did a good piece of hitting there. One of those kind of homers you tip your cap and move on. Those two walks still are irritating me right now."
Bellinger hit his 27th home run in the eighth inning for a 4-1 Dodgers lead. He belted a 3-0 pitch from reliever Rex Brothers into the right field bullpen.
Newcomb pitched well in spots but struggled with command and issued five walks while allowing three runs in six innings. He struck out nine and scattered three hits, but the walks proved to be his undoing.
NOTES: Dodgers 3B Justin Turner has bronchitis, but he returned to the starting lineup Sunday after missing Saturday's game. With his 10th-inning single, he has hit safely in 19 consecutive games ... Braves OF Matt Kemp has hit safely in nine of the past 10 games. He singled in the ninth and was 1-for-4. ... Dodgers INF Adrian Gonzalez, on the disabled list due to a back injury, took batting practice and told manager Dave Roberts he felt good.