The eighth-seeded Matisse needed three sets to down Japan's Go Soeda 6-4, 3-6, 6-3 with the help of 18 aces.
Levine, meanwhile, also moved on to the second round with a 7-5, 6-2 decision over American Bradley Klahn in the day's only other main draw match.
Two-time defending champion Milos Raonic of Canada is the top seed in San Jose, while John Isner of the United States is seeded No. 2 in the event.
Florida bear attack: Black bear mauls woman's face
Toddler uninjured after being knocked over by Obama family dog