Having struggled to overcome Tonga 28-19 earlier in the day, Wales were up against it from the outset against Fiji in stifling heat when centre Adam Warren was sent to the sin bin inside the first two minutes.
Jasa Veremalua made Wales pay by slicing over to give Metuisela Talebula an easy conversion during his absence.
Wales refused to buckle under the abrasive Fijian barrage and replied when Gareth Davies scrambled over in the corner. Alex Webber then stepped his way over shortly after the break before Rhys Shellard combined superbly with Lee Williams to send the latter over. With Davies adding two conversions Wales had jumped out to a 19-7 advantage.
Levani Botia then ensured a nerve racking end when he scored a converted try to bring the favourites to within touching distance but immaculate defence held Fiji at bay.
"The first two games were all about points difference but we went into that game knowing we had to get the win but that was a performance we knew we had in us," said a delighted Wales skipper Adam Thomas.
"If we show that sort of consistency tomorrow anything can happen," he added.
Every member of the Welsh squad produced the goods when it mattered in both games - with James Davies catching the eye again with his turn of pace and defence.
While finishing top of the pool may have surprised some, Wales assistant coach Gareth Williams was quick to declare that the win against Fiji was no fluke.
"We know the quality is there, but their work ethic and physicality against a top Fijian side was outstanding," added Wales assistant coach Gareth Williams. "The self-belief is there for all to see so hopefully we can carry on tomorrow where we left off today."