Gabby Williams led the Hungarian team to victory with 16 points at the Ulker Sports and Event Hall in Istanbul.
Both sides were former runners-up of the EuroLeague Women tournament, but Sopron came out on top and got their maiden title.
Fenerbahce have now become the runners-up for the fourth time in the tournament.
Earlier in the day, Spain's Perfumerias Avenida beat Czech team ZVVZ USK Prag in the match for third place.
