Tusi Pisiata gave Samoa an unanswered 12-point lead in the first half. The fly-half kicked the first of his three penalties before the break in the fifth minute and added a drop goal to his tally soon after.
Within five minutes of the restart, Pisiata kicked a fourth to further extend Samoa's lead. Fiji still had no answer as Kahn Fotuali'i added a try on the hour-mark to take the score to 20.
Next up for Samoa is South Africa on Friday.