Atlanta (93-49) reached the postseason for the sixth straight year, the second-longest streak in franchise history. The Braves won 11 straight NL East titles from 1995 to 2005.
Entering Sunday, the Braves held a 14-game lead over second-place Philadelphia in the NL East.
Ronald Acuna Jr. had a key two-out single to spark the seventh-inning rally and had two RBIs.
Brad Hand (4-1) won in relief of rookie Allan Winans, who allowed two runs and six hits while striking out eight in 6 1/3 innings. A.J. Minter struck out the side in the eighth, and Raisel Iglesias pitched a scoreless ninth for his 29th save in 31 chances.
Bryan Reynolds and Jake Suwinski had RBI doubles in the sixth. Olson's run-scoring groundout cut the deficit in the sixth.
With the Braves trailing 2-1 in the seventh and chants of "M-V-P" being heard across Truist Park, Acuna hit a two-run single over Suwinski that short-hopped the center-field wall. Olson followed with a two-run single.