Wood issued his four walks in the first three innings, but he worked around Asdrubal Cabrera's leadoff double in the fourth and Kipnis' two-out double in the fifth.
A two-out single by Michael Brantley chased Wood in the sixth. The next Atlanta pitcher, Luis Ayala, walked Stubbs, the only batter he faced, but Scott Downs ended the threat by striking out pinch-hitter Jason Giambi.
Cabrera went 3 for 4 and was the only batter with more than one hit, but Johnson drove in the game's only runs.
"I got a fastball out over and hit it well enough to get it over Stubbs' head, and we get a couple of runs off a guy that throws really hard," Johnson said. "But Woody was the story of the day, pretty much commanding all of his pitches and keeping them off balance."
Gonzalez indicated that Johnson, claimed off waivers last week from Kansas City, likely will stay with Atlanta with second baseman Dan Uggla set to come off the disabled list on Wednesday.
Johnson started his fifth game at second base in Uggla's place.
Notes: Braves RF Jason Heyward rejoined the team for the first time since getting hit by Mets pitcher Jonathon Niese last Wednesday, breaking the right side of his jaw with a 90 mph fastball. Heyward hopes to return for the playoffs. ... Atlanta RHP Brandon Beachy was in the clubhouse one day after learning there's no structural damage in his surgically repaired elbow. Beachy, who has missed 109 games over the past two years, hopes to return by the end of next month. ... The Indians and Braves met for the first time since 2007 and for the first time at Turner Field since 2004. ... Uggla went 2 for 4 with a homer in his last rehab appearance Tuesday with Triple-A Gwinnett. ... Atlanta had its fewest hits in a victory since getting three on July 19, 2012, against San Francisco.