In a fiercely competitive group where Wales, Fiji and Kenya all had aspirations of making the quarter-finals, the defeat to the Africans was a major setback for Paul John's men.
Darren Daniel's first half try was all Wales could get out of the game which meant they had to score an avalanche of points in their last game against Papua New Guinea to give themselves a chance of going through.
Fiji had scored 41 unanswered points against the minnows of the pool while Kenya had accumulated 27. But John's men responded brilliantly by racking up a comfortable 64-5 victory in a 10-try romp to scrape through as top qualifiers from the pool.
A first half hat trick by Jevon Goves set up Wales runaway victory as Lloyd Williams and Rhys Jones chipped in with a try apiece while Jones banged over four conversions.
Darren Daniel kept the momentum going by racing over soon after the halftime whistle before Craig Hill (2), Jones and Ifan Evans completed the job.
Wales head coach Paul John paid tribute to his team who have made the quarter-final draw for the second tournament running.
"Overall to score 64 points against anyone in a tournament is outstanding," he said. "The boys were really professional about what they had to do. To score three tries early on and keep the foot on the gas was really good. They didn't let up at all.
"It was important to score as many points as possible, so it was mission accomplished in many ways. But the boys will be regretting the way we played against Kenya. Our defence was very good but our attack wasn't as good as it has been. So it was a bit up and down and a bit of a roller coaster but we got our reward with a quarter-final.
"Hopefully we can do better in this quarter final than we did last time against Samoa. We've got to keep playing in these games and hopefully we'll win one soon," he added.
Wales will now play USA, who were runners-up in Pool D, in tomorrow's quarter-final.