Beachy (1-1) struck out seven and walked two in his seventh big league start. The right-hander came in with a 5.19 ERA over his three previous outings this season, including a 6-5 loss on Thursday against Florida at Turner Field in which he was charged with five runs and four walks in 5 1-3 innings.
The Dodgers trimmed Atlanta's lead to 2-1 in the seventh against Scott Linebrink when Juan Uribe led off with a scratch single off Linebrink's glove and scored from third when third baseman Chipper Jones robbed rookie Jerry Sands of a possible double down the line with a diving stop and threw him out by a step.
The run ended a scoreless streak of 18 2-3 innings by the Braves' bullpen. Jonny Venters replaced Linebrink, striking out pinch-hitter Marcus Thames and retiring Casey Blake on a bases-loaded grounder after a two-out walk to Jamey Carroll.
The Braves blew it open with eight runs in the ninth. Hinske batted for Venters in the ninth and deposited Kenley Jansen's 3-1 pitch into the first row of the lower seats in the right field corner for a two-run homer.
It was Hinske's first home run of the season and sixth of his career as a pinch-hitter. He also capped the rally with an RBI single after Uggla's three-run homer off Ramon Troncoso and RBI singles by Brian McCann and Alex Gonzalez.
Hiroki Kuroda (2-2) allowed two runs and five hits in 6 1-3 innings, and was lifted with one on when Brooks Conrad came up as a pinch-hitter for Beachy. Kuroda lost a 1-0 decision to the Braves' Tim Hudson last August in Atlanta when Conrad homered against him in the seventh inning. The right-hander also pitched a one-hit shutout against the Braves at Dodger Stadium on July 7, 2008.
Kuroda, a control specialist who came in averaging 2.02 walks per nine innings during his four-plus seasons in the majors, walked his first two batters in the fifth before starting a 1-6-3 double play on Nate McLouth's comebacker and retiring Beachy on a groundout with Freeman at third.
But in the sixth, Prado led off with a drive that barely cleared the fence in left-center. The homer was just the second hit off Kuroda to that point, including Prado's leadoff single in the first. Kuroda got behind Freeman 2-1 before his next pitch cleared the fence just to the left of center field.
Conrad greeted Blake Hawksworth with a single, the first hit by Braves pinch-hitters this season in 26 at-bats to that point. Prado walked, loading the bases, but Jason Heyward grounded to first for a force at the plate and Jones popped out.
The Dodgers threatened in the first when Andre Ethier hit a two-out double to right field off Heyward's glove in the warning track. But Uribe grounded out after an intentional walk to major league batting leader Matt Kemp, who came in 10 for 19 with runners in scoring position. Ethier's hit extended the longest active hitting streak in the majors to 16 games and match the longest streak of his career, which he established as a rookie in 2006.
Beachy retired 10 of his next 11 batters after the walk to Kemp, striking out the side on 17 pitches in the fourth as Kemp, Uribe and James Loney all went down swinging.
Sands led off the Dodgers' fifth with his second double in two games since his promotion to the big leagues, but was erased at third on Kuroda's routine grounder to shortstop for the second out and Carroll flied out.