Captain Jonathan Edwards led by example with a brace of tries salvo before Dafydd Hewitt and Tal Selley crossed to set up a last-eight clash against Scotland at 12.50pm on Sunday (live on BBCi).
"It was a fantastic effort from all the players and they should be proud of their efforts," said Team Manager David Jenkins.
"We made it hard for ourselves by losing our first game but we showed great pride and determination to come back and win our remaining games. We will be going full out to win some silverware."
After an opening 24-14 pool defeat to South Africa, Wales faced an uphill struggle before Edwards starred in the must-win clash against the Red Rose.
They took that form into their final game as Martyn Thomas's double and James Merriman's late try secured a 15-14 win over Portugal to book their quarter-final spot.