The Dodgers won the series 3-1, and advance to the NLCS for the first time since 2009 against either the Pittsburgh Pirates or the St. Louis Cardinals.
"We've moved one step closer, and we don't have to get back on a plane tomorrow. It's a good feeling," said Mattingly.
Carl Crawford made sure Kershaw's start would not be in vein as he homered twice, once in the first and once in the third inning for the 2-0 lead.
Braves third baseman Chris Johnson connected on an RBI single that scored Freddie Freeman, and later Andrelton Simmons grounded into a fielders choice and Evan Gattis tied the game at 2-2 in the fourth inning.
After six solid innings by Kershaw who didn't give a run, was replaced by Ronald Belisario in relief who gave up a run to Jose Constanza, and Braves took the lead 3-2 lead in the seventh inning.
Brian Wilson pitched a perfect eight inning and was awarded the victory.
With Yasiel Puig on base after hitting a double, Juan Uribe connected on a two run home run after two failed bunt attempts for the 4-3 lead.
"This moment today, I'll never forget! I think a lot of people feel like that," said Uribe.
"The smile on his face when he hit that homer is priceless," Mattingly said.
Kenley Jansen slammed the door shut with a brilliant ninth inning for the save as Jansen and AJ Ellis celebrated the victory on the field.
"This team has a lot of fun. We don't think about being the team to beat and all that stuff. We just go out there and play and try to have fun," Crawford said.
With a sellout crowd, fans celebrated with the Dodgers, Kershaw, Puig, and some other players high fived and talked with fans as they ran across the field.
"They were loud," Kershaw said. "They want it just as much as we do." Kershaw continued about what this win meant to the team, "there's a handful of guys that have never gotten to do that before."
David Carpenter took the loss after he gave up the two run homer to Uribe.
"To end the way it did tonight, it's going to hurt. It's going to be a long way back," Fredi Gonzalez said. "But tip your hat to the Dodgers and congratulate Donnie and his staff."