Emosi Mulevoro scored the match-winning try with one minute remaining to beat Scotland 17-10 and seal a third-place finish for Fiji in the penultimate round of the IRB World Sevens Series in Glasgow.
Having qualified top of their pool, Fiji beat England 14-12 in the quarter finals but were knocked out of title contention by series leaders New Zealand in the semis.
Fiji's victory further cements their grip of third place in the overall series standings, with just one round remaining in London this weekend.
Meanwhile Samoa were beaten 29-12 by Argentina in the bowl semi finals to slip to eighth overall.
New Zealand all but secured a twelfth World Series title after thrashing Canada 54-7 in the Cup final, to extend their series lead over South Africa to 19 points with one round remaining.