The Cook Islands now face New Zealand in Christchurch next Sunday, while Fiji meet defending champions Australia at Suncorp Stadium the day before.
Those tests follow Fiji's 40-12 victory over the Cook Islands in their World Cup Pool A opener at McDonald Jones Stadium on Sunday.
Jacob Saifiti marked his return from suspension by scoring in the 28th minute, pouncing on Brandon Wakeham's kick and taking the ball from fullback Esom Ioka.
The Newcastle prop had missed four matches after a dangerous tackle against the Warriors in round 26, ending his Knights' finals campaign.
It was Saifiti's eighth Test for Fiji and his first match back from the ban; he is appearing at his second World Cup.
Fiji scored five first-half tries to lead 28-0 at the break, with Solomon Saukuru later claiming a double.
Skipper Api Koroisau guided the side with strong defence and attacking kicks, while halves Wakeham and Kurt Donoghoe combined for five line-break assists and five try assists.
The Cook Islands responded through Maui Winitana-Patelesio and Davvy Moale, who scored four minutes apart to narrow the margin to 34-12.