With one out in the seventh, Elliot Johnson tripled into the right-field corner, sending Puig sliding into the dirt chasing the ball as it caromed off the wall. Constanza, batting for starting pitcher Freddy Garcia, singled into center to put the NL East champions ahead for the first time.
Garcia allowed two runs and eight hits in six innings. He struck out six and walked two.
The Braves tied it 2-all in the fourth.
Crawford’s second homer of the game came in the third, landing deep in the lower right-field seats for a 2-0 lead.
Crawford led off the first with a towering home run to the right-field pavilion, smiling broadly as the Dodgers took a 1-0 lead.
“The smile on his face when he hit that homer is priceless,” Mattingly said.