Tom Koehler (1-0) pitched six innings, allowing two runs and Brad Hand pitched three scoreless innings for his first career save.
Stanton's two-run blast traveled an estimated 458 feet to left field, nearly leaving the stadium and giving the Marlins a 2-0 lead in the first inning.
It was Stanton's second home run. He has nine RBIs through five games while hitting .350.
Casey McGehee had two RBI's pushing his total to 10, which is the most by any Marlins player in the first five games of the season. McGehee had a sacrifice fly as part of a three-run third inning to stretch the lead to 5-0 and had an RBI single in the eighth to cap the scoring for Miami.
The Marlins have scored 35 runs in their 4-1 start after finishing last in the majors in runs last season during their 100-loss campaign.
On the other end is San Diego, which has scored eight runs in four games.
Garrett Jones also had an RBI double and Marcell Ozuna drove in a run for the Marlins.
Hechavarria, known more for his dazzling defensive plays at shortstop, is hitting .579.
Yonder Alonso and Gyorko drove in the runs for the Padres.
NOTES: Grandal, a Miami native, reached base four times and had approximately 150 friends and family members in attendance. . Miami Dolphins offensive tackle Brandon Albert threw out the ceremonial first pitch. . Marlins 21-year old ace RHP Jose Fernandez (1-0, 1.50) will make his second start of the season on Saturday against Padres RHP Andrew Cashner (0-0, 1.50).