The Pumas bounced back from their opening-game loss to England to kick off their campaign at a rain-soaked Stade Geoffroy-Guichard.
Boffelli, an Argentina winger, converted his own try and kicked three penalties.
Late in the game, Sama Malolo powered through to set up a tense finale, but Nicolas Sanchez’s penalty sealed victory.
Australia’s former fly-half Argentina led by 10 points at halftime after Christian Leali’ifano missed two of his three penalties.
Despite their only win over the Pacific Islanders, the Pumas remain fourth in the table, two points behind leaders England.
Line-ups
Argentina: Mallia, Boffelli, Moroni, Chocobares, M Carreras, S Carreras, Bertranou, Gallo, Montoya (captain), Bello, Pagadizabal, Alemanno, Matera, Kremer, Gonzalez.
Creevy, Vivas, Kodela, Rubiolo, Bruni, Cubelli, Sanchez, Cinti are the replacements.
Paia’aua, Ah-Wong, Seuteni, Manu, Lam; Leali’ifano, Taumateine; Lay, Lam, Alo-Emile, Alainu’u’ese, Vui (captain), McFarland, Lee, Luatua.
Malolo, Faumuina, Alaalatoa, Seu, Taufua, Matavao, Leuila, and Toala are the replacements.