Warm oil in a large pot with a tight lid over low heat. Add garlic and cook, stirring until golden, about 3 minutes. Add tomatoes, increase the heat to high and stir for 1 minute more. Pour in wine and bring to a slow boil.
Add mussels, cover and steam, occasionally giving the pan a vigorous shake, until alll the mussels have opened, 3 to 4 minutes. Discard any that do not open. Transfer the mussels to a serving bowl. Spoon broth over the mussels and sprinkle with parsley.