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Scrumhalf Kahn Fotuali'i and number eight George Stowers scored second-half tries - one of which was converted by fullback Paul Williams - for the Samoans, who dominated territory and possession against the error-ridden Fijians.
Fijian blindside flanker Netani Edward Talei crashed over for his side's only try after Fotuali'i scored to give them some hope of forging a late fightback but Stowers' immediate reply ended any chances they had of winning the game.
The sides had met 46 times in the past, though Sunday's game in Auckland, which is the largest Polynesian city in the world and provided a crowd of 60,000, had never met in the World Cup.