With the combined results of the 2016 and 2017 cups doubling as World Cup qualifiers, Samoa needed to at least draw with the unbeaten Fijians to overhaul Tonga and reach the tournament in Japan in two years time.
Even a bonus point in defeat might have been enough.
They led 16-14 at half time in Apia but had no answers as Fiji over-ran them in the second half.
Fiji, who secured qualification last week when they defeated Tonga 14-10, scored five tries in total, including a hat-trick to scrumhalf Henry Seniloli.