However Wales were given a scare or two along the way and it looked as if Warren Gatland's reign as coach could be brought to an end in his home town.
Samoa had led 10-6 at the break and had enjoyed numerous phases in the Wales half, but they were unable to turn all the pressure into points.
Anthony Perenise scored their only try, with Paul Williams adding five points from the boot.
However six points apiece from James Hook and Rhys Priestland and a crucial second-half try from Shane Williams ensured Wales kept their World Cup hopes alive.
Samoa got off to a slow start as first Tasesa Lavea's kick-off went out on the full, while the resulting scrum collapsed. Fortunately Hook was off target with a long-range effort.
Having escaped, Samoa set the tone for the game as they hammered away at the Wales defence.
They first spurned an overlap chance with the last pass going to ground, while George Stowers was stopped short after the pack had turned over a Wales scrum.
Wales, though, were able to relieve the pressure when Hook landed a straightforward penalty from 25m after a high tackle on Priestland, but Williams responded with a three-pointer of his own.
The Welsh had the odd moment of their own going forward with Jamie Roberts in particular up for the physical challenge.
And although Priestland missed a drop-goal attempt on 22 minutes, Hook was able to put them back in fromt with a penalty after the Samoa scrum crumbled.
Despite clearly having issues in the scrum, the Samoans had no such problems in the breakdown - with their pack happy to hammer away around the fringes of the breakdown to drive Wales back.
And they were left frustrated when an 18-phase spell ended with Maurie Fa'asavalu burrowing over from close range, only for the flanker to be pinged for a double movement.
A missed penalty from Williams soon after did little to lift the mood of the Samoans.
However the Pacific Islanders finally got the try they deserved with new Bath prop Perenise profiting deep into first-half injury time after another long spell of pressure on the Wales line. Williams converted to put Samoa 10-6 up.
There was further bad news for Wales as they lost Hook at the break - but Priestland took over the kicking duties to cut the deficit to a point, albeit via the crossbar.
Williams had the chance with a penalty of his own after 48 minutes but his kick drifted wide.
And Wales made them pay as they regained the lead through Priestland's second successive attempt before Shane Williams put the result beyond the Samoans. Leigh Halfpenny made the initial break from Lavea's up and under and although he was unable to take the return pass from Jonathan Davies, Williams was on hand to finish.
Samoa regrouped and continued to hammer away at the Wales line but they couldn't find a way through.
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