After securing victories over Zimbabwe and Portugal, Wales jumped out to a 14-0 lead against the world series pacesetters but Fiji showed why they are such a force to be reckoned with in the abbreviated game to roar back with five unanswered tries to record a 29-14 triumph.
Wales will begin day two in the Cup quarter-finals with a match against Samoa who topped Pool A with wins over England, Argentina and USA. Paul John's men have played the South Sea Islanders once this campaign, winning the Plate Final 26-15 in the opening leg of the HSBC World Series in Australia two weeks ago.
Earlier Owen B Williams also scored twice in both of Wales' victories - 42-7 against Zimbabwe and 34-7 over Portugal - to set up the crucial decider against Fiji.
Despite the defeat to Fiji, Wales Sevens head coach Paul John was delighted to see his young side reach the main draw for the second day's action.
He said, "It was a great achievement by the side to get through to the quarter finals for the third week on the trot. It was fully deserved as I thought they played well all day.
"We got two good wins against Zimbabwe and Portugal - who won the FIRA competition in the summer. Once again we pushed Fiji all the way, going 14-0 up. With the opportunity to go further ahead we made a couple of unforced errors and they showed what a great team they are to fully capitalise.
"We now have another opportunity tomorrow against Samoa who topped their group. It would be a great achievement to go at least one step further tomorrow. This side has already proved they are a match for anyone when they believe in themselves."