Fiji dominated possession and territory in the first half. Wales's attack looked pedestrian and blunt compared to the South Sea islanders and paid the price with Nemani Nagusa and Osea Kolinisau scoring first half tries.
Fiji showed their pedigree in the second half by denying Wales the ball and slowing down the game at every opportunity to frustrate the Welshmen. Metuisela Talebula sealed the win when stretching away from the Welsh defence in the dying stages of the match.
As expected the Pool was the most competitive group in the New Zealand leg with Tonga surprisingly finishing top after holding Wales to a 14-14 draw and beating their Pacific Island counterparts Fiji 17-14 and Argentina 24-14.
Wales had earlier beaten Argentina 19-7 so went into the match against Fiji knowing that the winner would go through to the knockout stage on day two. However it was not to be as Fiji turned the screw from the outset to waltz through while Wales will begin day two in the Bowl draw with a match against United States.
Wales Sevens head coach Paul John reflected afterwards on a chance missed to reach the knock out stages.
"It was a disappointing day overall," he said. "Not to qualify for the quarter-finals is very disappointing. We had chances to beat Tonga in our first game and had we won it we would have gone through.
"We played better to beat Argentina in our second game and there wasn't a lot in it against Fiji in our last game. The boys battled hard and made it difficult for them.
"We now need to re-group and keep to the same performance level to progress in the Bowl tomorrow."