It was a throwback to Fiji's glory days as they showcased their full artillery of sevens weaponry to counter the strong Samoans with overhead and no-look passes and scooping the ball off the ground one-handed.
The win lifted Fiji to within four points of series leaders New Zealand, who won the first two rounds in Dubai and George, South Africa, before falling to Samoa in the semifinals here.
Samoa have moved up to third ahead of England, who were beaten by Fiji in the semifinals, with Australia fifth.
The final was locked at 7-7 at halftime after Jiuta Lutumailagi put Fiji in front in the opening minute and Mikaele Pesamino replied for Samoa with a clever kick-and-chase move midway through the spell.
Samoa, without veteran playmaker and captain Lolo Lui, who was suspended after a dangerous tackle in the semifinal against New Zealand, appeared to lose their way against the Fijian artistry for most of the second spell.
Tries by Emosi Vucago and Osea Kolinisau saw Fiji race to a 19-7 lead before the Samoans regrouped with a minute to go and fought back with a second try to Pesamino. They were pressing the Fiji line again when the final hooter sounded.
The fourth round of the IRB Sevens series will be played in Las Vegas next weekend.
The standings: New Zealand 64 points; Fiji 60; Samoa 46; England 44; Australia 30; Kenya 28; South Africa 24; Argentina 22; Wales 12; Canada 6.
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