Matt Lindstrom (3-2) got the win after pitching the top of the ninth for Florida.
Florida starter Josh Johnson gave up three runs on nine hits without walking a batter while striking out eight in six innings.
Josh Anderson had three hits and an RBI and Brandon Jones was 2-for-3 with an RBI and a run scored for Atlanta.
Braves' starter Mike Hampton matched Johnson over six innings, allowing three runs on six hits and three walks.
In the ninth, Mike Gonzalez (0-1) issued a leadoff walk to Dan Uggla, who moved to second on a sacrifice by Josh Willingham. Gonzalez then intentionally walked Cody Ross before unintentionally walking Wes Helms to load the bases, setting up Baker's game-winning fly to left.