Craig Kimbrel came on to record a four-out save after the Dodgers had inched within a run in the eighth, allowing the Braves to deadlock the National League Division Series at 1-1.
The series resumes on Sunday in Los Angeles, where the Dodgers won 47 times this season. Atlanta was the only team to make the playoffs this year with a losing road record.
After scoring only one run in a series-opening loss to the Dodgers, Atlanta scratched out two runs in four innings against Zack Greinke to take the lead.
Andrelton Simmons had an RBI double in the second to overcome an early Los Angeles lead and Chris Johnson singled home another run in the fourth.
Atlanta still had a 2-1 cushion in the seventh, an inning in which the Braves loaded the bases with two away. After Reed Johnson was walked intentionally to get to Heyward, the Atlanta leadoff hitter singled to center to bring home two runs.
Mike Minor allowed a lone run on eight hits over 6 1/3 innings to get the win, but the Braves' David Carpenter walked Mark Ellis to open the eighth and Hanley Ramirez homered to cut the Dodgers' deficit to a single run.
Carpenter then struck out two batters before giving way to Kimbrel, who tied Baltimore's Jim Johnson for the major league lead in saves this season with 50.
Kimbrel got Juan Uribe on a ground out to end the eighth and then gave up a one-out walk to A.J. Ellis in the ninth. Ellis, however, was thrown out trying to steal second. Kimbrel issued another walk to Andre Ethier before striking out Carl Crawford to end the game.