Atlanta's victory also guaranteed a playoff spot for the Boston Red Sox, the sixth team to secure a post-season berth with a week remaining in the six-month campaign and six spots unclaimed.
"We've been fighting all year to get to this moment," Braves pitcher Martin Perez said. "And we're not done yet."
The Braves improved to 92-64 to take their first National League East division crown since 2023 while Houston's loss ensured an American League wildcard playoff berth for Boston despite a 5-1 loss at Tampa Bay.
"We never stopped believing in each other," Boston outfielder Wilyer Abreu said. "That's why we're here."
The Chicago Cubs, who cruised 9-1 at Cincinnati, reached the brink of a National League playoff spot but missed out when Arizona rallied to beat the visiting New York Yankees 8-4.
Entering Sunday, the Braves, Yankees, Tampa Bay, Milwaukee and the Los Angeles Dodgers had clinched playoff berths, the Dodgers taking a 13th NL West title in 14 seasons and Milwaukee capturing the NL Central crown.
Host Houston grabbed a 1-0 lead over Atlanta in the fourth inning on Jose Altuve's solo home run.
The Braves, however, answered in the sixth when Ozzie Albies singled in a run and Yastrzemski followed with a three-run homer for a 4-1 Atlanta lead.
Yainer Diaz smacked a solo homer for the Astros in the eighth but Braves left-handed relief pitcher Dylan Dodd struck out the side in the ninth to give Atlanta the triumph and start the team celebration.
"When we faced our biggest challenges, that's when we've been at our best," Braves manager Walt Weiss said.
"You've got to get in and then you take your best shot. I think we've got to keep our foot on the gas."
'To hell with that'
The Red Sox, 84-72, began the season 32-46 and seemed destined to miss the playoffs, but Boston responded after manager Alex Cora was fired April 25 and replaced by interim manager Chad Tracy.
"You stared impossible in the face with the position we were in and you beat it back. You said to hell with that and we're going to go to the playoffs," Tracy told his team after the bid was secured.
They didn't mind 'backing' into a post-season spot after a defeat.
"To fight as hard as we did, to put ourselves in the position we did, I don't think you care much how it gets done," Tracy said. "You just want to see your ticket get punched."
At Arizona, the Yankees took a 4-1 lead in the third inning on solo homers by Heliot Ramos and Spencer Jones and George Lombard's two-run homer.
The Diamondbacks seized a 6-4 lead in the fifth inning on a bases-loaded walk followed by a grand slam homer by Nolan Arenado.
Arizona's Geraldo Perdomo added a run-scoring triple in the seventh and scored on a Corbin Carroll single to create the final margin.
The Cubs routed the Reds as Pete Crow-Armstrong went 3-for-5 with a home run and three runs batted in.
The Cubs reached the brink of a playoff berth as Pete Crow-Armstrong went 3-for-5 with a home run and three runs batted in against the Reds.
Cubs third baseman Alex Bregman, hitting .260 with 26 home runs and 88 runs batted in, left the game in the fourth inning after being struck in the face by a foul ball while standing in the on-deck batter's circle.
"He had a cut under his eye," Cubs manager Craig Counsell said. "He was bleeding from his nose a little bit. It's pretty swollen. It was below the eye... It's just an unfortunate accident. I'm hoping and praying he's all right."