Ramon Hernandez started the rally with a one-out single, took second on the first wild pitch and advanced to third on a single by Luis Cruz.
Varvaro (3-1) then bounced another wild pitch to Juan Uribe, allowing Schumaker to score. Dodgers rookie Yasiel Puig was on-deck, but he wasn't needed after homering for the fourth time in five career games.
Brandon League (2-2) got the win in relief.
The Dodgers have won four of five since Puig was called up on Monday from the minors. It was their second straight win over the NL East-leading Braves, who lost for the first time in six games on Thursday.
With a runner on second in the 10th, Justin Upton grounded out to catcher Ramon Hernandez, who fired the ball to first base. Umpire CB Bucknor called Upton out to end the inning, although the replay clearly showed he had beaten the throw. Braves manager Fredi Gonzalez came out to argue to no avail.
The Dodgers had the potential go-ahead run on third with two outs in the eighth when reliever Jordan Walden intentionally walked Puig, the first time this week a team didn't want to pitch to the rookie. Mark Ellis flied out to end the inning.
Puig tied the game 1-all with his fourth homer and 10th RBI of the week with two outs in the sixth. He sent an 0-1 pitch into the left field pavilion not long after being shown losing the "Chopstick Challenge" on the video board. He managed just 12 points competing against a female fan in moving baseballs from one bin to the other using chopsticks.
Puig tied the record for most RBIs through five career games, shared by Danny Espinosa (2010) and Jack Merson (1951), according to information provided to the Dodgers by Elias Sports Bureau.
The Braves led 1-0 on Dan Uggla's RBI single with two outs in the fourth.
Hyun-Jin Ryu returned to the mound after missing his last start for the Dodgers. He bruised his left foot on May 28 against the Angels, when he tossed the first shutout of his career in a 3-0 victory. The left-hander allowed one run and six hits in 7 2-3 innings, struck out six and walked one.
Paul Maholm gave up one run and four hits in 7 1-3 innings, struck out three and walked two.
NOTES: Puig is the second player since 1900 to hit four homers in his first five games, joining Mike Jacobs of the New York Mets in 2005, according to Elias. ... Dodgers INF Hanley Ramirez was out of the starting lineup for the second straight game on Friday because of tightness in his left hamstring, but he pinch-hit in the ninth. "For me it's a concern because it's two days," manager Don Mattingly said. The same hamstring landed Ramirez on the DL earlier this season. ... Dodgers LHP Ted Lilly is in doubt to start Sunday's series finale. He was bothered last time out by a chronic neck issue and Mattingly said if Lilly can't make his start, a minor leaguer would be called up. ... Braves RHP Brandon Beachy will make his fourth injury rehab start on Saturday for Triple-A Gwinnett.