Cruz gave the Dodgers a scare when he left the game with an apparent leg injury in the seventh. He said he slowed when he felt a cramp starting and should not miss any time.
"I'm very happy the initial evaluation was a cramp," said bench coach Trey Hillman, who filled in as manager Don Mattingly completed a two-game suspension for excessive arguing with plate umpire Angel Campos in Thursday's 10-6 loss in Pittsburgh.
Billingsley (10-9) gave up three hits in seven innings, striking out four and walking two. He is 6-0 since the All-Star break after losing five straight. He reached 10 wins for the sixth straight season.
The right-hander started his winning streak following his return from the disabled list with right elbow inflammation.
Billingsley is the first Dodgers pitcher to win six straight starts since Kevin Brown won seven straight in 2003.
The Dodgers return home to open a series Monday night against San Francisco for the NL West lead.
Heyward tripled with two outs in the fourth for Atlanta's first hit. Billingsley walked Freddie Freeman before Dan Uggla popped out.
The Braves' only other scoring opportunity against Billingsley came when Michael Bourn singled with one out in the sixth, stole second and moved to third on Martin Prado's grounder. Heyward struck out to end the inning, and then tossed his bat and helmet in frustration.
Braves catcher Brian McCann was 0 for 3 after sitting out two straight games. He said Saturday he has a cyst and a frayed labrum in his right shoulder but can play through the discomfort. He is hitting only .103 (4 for 39) in August and .227 overall.
NOTES: Braves SS Andrelton Simmons, on the 15-day DL since July 13 with a broken right little finger, still hasn't been cleared for baseball activities. ... RHP Tim Hudson will look for his 13th win when he faces Washington's Jordan Zimmermann on Monday night. Dodgers LHP Clayton Kershaw will face the Giants' Madison Bumgarner on Monday night.
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