Capuano (2-0) limited the Braves to one run on six hits, overcoming four walks and striking out five as the National League West-leading Dodgers improved to 13-4 to start the season.
Uribe contributed a run-scoring single and later scored in the second inning, putting Los Angeles ahead to stay, and added a two-run hit in the eighth.
Andre Ethier went 3-for-4 with an RBI and A.J. Ellis drove in a pair for Los Angeles, which improved to 7-0 at home in the first of a six-game homestand.
Atlanta's Jair Jurrjens (0-2) was roughed up for nine hits over a three-inning start, allowing five runs.