Iwakuma (4-2) gave up only six hits with seven strikeouts and no walks in seven innings. The right-hander was sharp, throwing 71 of his 96 pitches for strikes.
Mike Minor (2-4) allowed only one run in seven innings, but the Braves fell to 0-6 in interleague games.
Yoervis Medina pitched a perfect eighth before Fernando Rodney earned his 16th save with three straight outs in the ninth.
The Braves were held scoreless in the final seven innings of Tuesday night's 7-5 loss to Seattle. The streak of consecutive scoreless innings reached 16 on Wednesday.
Iwakuma, a 2013 All-Star, gave up a combined nine runs in back-to-back losses to Houston and Detroit before returning to form against the Braves.
Atlanta left runners in scoring position in the first and second innings and then didn't have another hit until the sixth, when Jason Heyward hit a leadoff single.
Minor allowed only five hits and one run in seven innings. He matched his season high with 10 strikeouts.
Seattle managed only one hit off Minor in the first three innings before taking a 1-0 lead with three hits in the fourth. Robinson Cano and Stefen Romero started the inning with singles before Gillespie's two-out, hit-and-run single to left field drove in Cano from second base.
Freddie Freeman had three strikeouts against Iwakuma and finished 0-for-4.
Braves manager Fredi Gonzalez unsuccessfully challenged first-base umpire Will Little's ninth-inning call that Justin Upton was out at first base on the throw from shortstop Brad Miller. The review lasted only 40 seconds.
NOTES: Seattle also won five straight from May 3-7. ... Willie Bloomquist hit leadoff for Seattle and made his first start at first base since 2010 with Kansas City. The versatile Bloomquist also has started at second base, third base, shortstop, left field and right field this season, and he is the emergency catcher. ... Seattle players wore T-shirts honoring trainer Rick Griffin's 5,000th regular-season game. He joined the team in 1983. ... The Braves and Mariners are off on Thursday. The Braves open a weekend series at Arizona on Friday, when RHP Julio Teheran faces RHP Brandon McCarthy. Seattle's east coast swing shifts to Tampa Bay, when Mariners RHP Chris Young will face LHP Erik Bedard.