With the Braves leading 4-2 in the fifth, Uggla kept his streak alive by collecting a leadoff infield single off Brad Hand (1-4).
Chipper Jones followed with another single and Gonzalez then blasted his 10th homer of the season to break the game open.
Uggla's is the longest active hitting streak in the majors and is one short of this year's season-high, posted by Los Angeles Dodgers outfielder Andre Ethier. It's also tied for the second-longest in Atlanta history with Rowland Office (1976).
Derek Lowe (7-10) earned the victory, holding Florida to two runs on six hits over six innings. Craig Kimbrel picked up his 35th save for the Braves.
John Buck hit a two-run homer and Greg Dobbs added a solo shot for the Marlins.