Wales had the perfect start to the game when Bramwell raced over in the first minute. The men in red held the dangerous Samoans at bay for several minutes but eventually Alafoti Fa'osiliva spotted a gap to cross over.
Fa'osiliva raced over immediately after the halftime break to give Samoa a 12-5 lead after Lolo Lui added the conversion.
Fautua Otto added a try in the sixth minute to put clear daylight between the two sides for the first time. Shellard went over late on but Samoa held on to move into the semis where they beat Australia 14-12 before producing a superb display to beat New Zealand 33-12 in the final.
Wales then moved into the Plate where Fiji cruised to a 32-0 victory after leading 17-0 at the break.
The Cup victory was only Samoa's fourth in the 11-year history of the IRB Sevens World Series and moved them up to second behind New Zealand in the 2009/10 World Series standings, just ahead of Fiji in third. Wales are now ninth in the overall standings with 18 points.