With the game in the balance at 18-16 at halftime, Fijian halfback Henry Seniloli (three tries) and Ben Volavola (13 points) secured the win for the visitors.
Fiji had sealed its own qualification for the 2019 World Cup in Japan ahead of Saturday's match. But Samoa needed at least a bonus point in defeat to prevent Tonga claiming the second automatic qualifying place from Oceania.
