Wales, who edged last season's IRB World Sevens Series champions New Zealand 15-14 in the quarter-finals, ran out 19-12 victors over a Samoa team visibly wilting after their dramatic sudden-death last-eight win over hot favourites England.
Aled Brew opened the scoring for Wales with an early solo try and fellow winger Tal Selley doubled the lead soon after.
Samoa hit back with a try from Alafoti Faosilivia, but the Welsh responded in the second-half with a third try from Tom Isaacs. Morgan Salesa claimed a late consolation try.
"It's unbelievable," said Isaacs, who also scored the decisive try against New Zealand. "We have worked so hard the last few months and credit to the coaches and all, but we deserve this and are just really happy to be here.
"We knew we have a strong squad and each of the 12 boys involved have played a huge part in every game. We have got depth coming in off the bench."
Samoa coach Rudi Moors rued a series of missed scoring chances.
"We had a lot of opportunities and we didn't use them and now it's over," he said.
"We probably left it a little bit too late in the end but we had some really good field positions which we didn't make the most of. They did their best and I am very pleased that we made it to the Cup semi final."
Kenya sensationally beat defending champions Fiji in the quarter-finals but could not continue their giant-killing against a rugged Argentina side.
The Pumas scored tries from Horacio San Martin and Martin Bustos Moyano in each half and successfully closed down the free running game of the Africans.
South Africa, currently joint leaders of the IRB World Series Sevens with England, exited in the quarter-finals at the hands of Argentina, winners of the most recent leg of the global circuit in San Diego last month.
England coach Ben Ryan admitted his side's defeat to Samoa in the last eight had been "a pretty bitter pill to swallow. It is certainly the most disappointing moment to date".
"I am hugely disappointed for the players because this was a World Cup-winning side that we had got together and they showed that last night and they showed it up until extra time when we came roaring back into it, when we just made a couple of the wrong decisions.
"But we didn't hold on to the ball. Extra time is all about holding on to the ball and making sure that we create an opportunity and don't force things - there is no need to."