Fiji will meet the Kangaroos next, while Cook Islands face New Zealand, after the Bati opened their World Cup campaign with a 40-12 win.
Fiji held 62 per cent of possession and led 28-0 at halftime, with their forwards dominating through the middle.
Brandon Wakeham contributed three try assists, two line breaks, four tackle breaks and six goals, while directing play with his kicking.
Apisau Koroisau also proved influential from dummy half as Fiji scored twice in the opening 12 minutes.
Jacob Saifiti scored his first Test try in the 28th minute, leaping above Cook Islands fullback Esom Ioka to claim an aerial ball.
Taane Milne burrowed over from dummy half five minutes before halftime, then Caleb Navale ran 40 metres to score from a Wakeham pass.
Cook Islands showed resilience but struggled to convert attacking chances, and Fiji's defence pressured them on the final tackle.
Kitione Kautoga extended Fiji's lead after the break before Maui Winitana-Patelesio and Davvy Moale scored for the Aitu.
Solomone Saukuru crossed from a Kurt Donoghoe pass with 10 minutes remaining, ending any prospect of a Cook Islands comeback.