Wales held a commanding 19-0 lead the break with Welsh set-piece completely dominating their opposite numbers to give Tom Prydie plenty of goal-kicking practice. The Dragons bound winger responded with four penalties and added a straight forward conversion to a penalty try to put Kirby Myhill's men firmly in control at the break.
However after the re-start, with a couple of additions to beef up their pack, Argentina proved a different proposition.
Two further penalties by the reliable Prydie put Wales 25-3 ahead after Pumas skipper Sebastián Poet had put his side on the board shortly after the interval with an easy shot at goal.
But a late rally by the resurgent Pumas saw the impressive Facundo Isa and centre Juan Cappiello score converted tries in quick succession to leave Wales under the kosh in the dying moments after replacement prop Gareth Thomas was forced to look on from the sidelines after being sent to the sin bin for tackling a player in the air.
The Welsh defence re-grouped to deny Argentina any further try-scoring opportunities to earn their best ever placing in the tournament.
Argentina tried to use their muscular pack in the first half but Wales held the upper hand in the scrums, often disrupting the set-piece to dismantle the Pumas hopes. Their cause wasn't helped when they were reduced to 13-men with both Joaquin Camacho Juan Cruz Guillemaín receiving yellow cards to leave Argentina stretched.
Wales' pack stood up to their much vaunted opposition with Ellis Jenkins enjoying a fine game on the side of the scrum while halfbacks Tom Habberfield and Matthew Morgan dictated play well to peg back Argentina with well judged kicking.
Wales finished seventh last year but a shock 9-6 victory over defending champions New Zealand in the pool stages, along with pool wins over Fiji and Samoa, before a semi-final defeat to the Baby Blacks, ensured Myhill's men finished the campaign on a high.
Wales: Try: Pen Try; Con: Prydie Pens: Prydie (6)
Argentina: Tries : Isa, Cappiello; Cons: Paz (2); Pen: Poet