Tommy Hanson (4-3) allowed one run in five innings with nine strikeouts and Martin Prado, Freddie Freeman and Dan Uggla each had an RBI in a three-run seventh. The Braves had lost seven in a row in St. Louis before Friday and swept the Cardinals for the first time since Sept. 11-13, 2009, also in St. Louis.
Lynn (6-1) missed a chance to become the franchise's first pitcher to win his first seven starts of the season dating to 1920, according to STATS LLC.
Carlos Beltran homered for the sixth time in six games with his league-leading 13th of the season and Allen Craig hit a three-run homer off Cristhian Martinez in the ninth for his third hit of the game.
Rafael Furcal had three hits and a walk to extend his hitting streak to 12 games, but the NL Central leaders struck out 14 times and stranded 10 runners while getting swept for the first time.
The Braves totaled 56 runs during a 7-2 trip, including a pair of extra-inning victories, and also swept a three-game series at Colorado. Since losing its first four games of the season, Atlanta is a major-league best 22-9 with four road series wins.
The Cardinals had runners on first and second with none out in the first before Hanson found his stride, and he struck out five of the next seven batters. Hanson fanned cleanup hitter Craig twice and permitted just one runner in scoring position the next four innings before tiring in the sixth.
Lynn threw a season-high 121 pitches in six innings, retiring his last eight in order. He's among three Cardinals to win their first six starts, along with Bob Tewksbury (1994) and Max Lanier (1946).
Lynn needed 26 pitches to escape unscathed in the first after the Braves put the first two on, and threw 39 more in the third. Heyward, whose 12th inning two-run homer was the go-ahead hit on Friday, fouled off three pitches on a full count before his bases-clearing double.
Lynn struck out seven and has struck out 27 in 25 2/3 innings his past four starts.
Beltran led off the sixth with his 13th homer, and Craig and Lance Berkman followed with singles to chase Hanson. Eric O'Flaherty struck out pinch hitters Matt Holliday and Tyler Greene, the last with the bases loaded, to end the inning.
The Cardinals were outscored 14-6 the last two games of the series.
Berkman, activated by the Cardinals from the 15-day disabled list from a calf injury before the game, was 1 for 5 with two strikeouts.
Chipper Jones entered in a double switch in the sixth and was 0 for 1 with a walk in his final regular season appearance in St. Louis. The 40-year-old Jones is retiring after the season.
NOTES: Furcal and Braves leadoff man Michael Bourn, who had two singles and an RBI in the eighth, have 51 hits apiece. Bourn entered the day leading the league in hits. ... Greene is 2 for 17 for his career as a pinch hitter and Holliday is 4 for 20. ... A standing room crowd of 45,729 lured by a David Freese bobblehead giveaway, with hundreds standing in line 2 1/2 hours before game time, was the Cardinals' seventh sellout. ... Beltran is 9 for 25 with six homers, a double and triple and 13 RBIs his past six games. ... Lynn's previous pitch high was 110 at Chicago on April 25. ... Craig's homer was the first allowed by Martinez 10 appearances.
Link to boxscore: Atlanta 7 at St. Louis 4