Aled Brew got Wales off to a perfect start when he burst through two defenders under the scorching sun to cruise home under the posts to give Aled Thomas an easy conversion.
Wales's, who began the tournament as 80/1 outsiders, saw their chances improve further when Richie Pugh finished off well after good work by Brew and Lee Williams.
Samoa hit back on the stroke of halftime when Alafoti Faosiliva raced over for Lolo Lui to add the extras to leave the contest evenly poised.
Wales harried and hunted the Samoans who were feeling the pressure in the second half. The south Seas Islanders found it hard to break the stranglehold the Welsh had on them and speedster Tom Isaacs put clear daylight between the two sides when he sliced through between two defenders to race in under the sticks to give Thomas another easy conversion
Morgan Salesa then pegged back another five points but it wasn't enough as Wales celebrated another remarkable victory on the way to the final where they face Argentina.