The Welsh led 19-0 at half-time, but substitute Osea Kolinisau landed three tries to extend Fiji's record haul of titles to 12.
The match was not without controversy, however, as the Wales-dominated first period saw Lee Williams spear-tackled onto his head by Ilai Tinai, who somehow received a yellow card rather than red for the dangerous offence.
And though Wales scored a third try with Tinai off the pitch, Fiji's half-time changes paid off and Kolinisau had his first try within a minute of the restart.
His third saw a tap penalty from inside his team's own half lead to the winning try, converted by Emosi Mulevoro.
England meanwhile reeled off three impressive victories to ease some of their pain on the final day.
They overpowered France 42-7 and South Africa 26-14 - fifth and second in the Sevens World Series respectively - and then cruised past hosts Hong Kong 42-7 to win the Bowl competition. The performances were completely at odds with the pool stage defeats against Samoa and Scotland which forced them out of the Cup quarter-final places.
"We weren't particularly bothered who we played today," said head coach Ben Ryan. "It was all about us and about putting in a performance and setting the bar to the right standard."
He added: "I want the standard to be higher and I'm hoping there's permanent change now because our first two games weren't good enough.
"The one thing we demand is consistency of performance and I'm hoping now that we have the potential to do that and finish the season on a high."
The Tokyo Sevens take place next weekend.