Contepomi, the Leinster fly-half, was impressed how Wales bounced back from a record 62-5 drubbing to England and a fortnight of stinging criticism.
Wales raced into a 24-7 half-time lead against Argentina with
tries from Gareth Thomas, Alun-Wyn Jones and Mark Jones and then held on defiantly as the Pumas hit back to dominate after the interval.
Contepomi said: "I think Wales will take a lot out of this game. They lost by 60 points to England but showed they can play against a tough team.
"There has been a lot of criticism of the coach and the players but if I was a Welshman, I would sleep in peace.
"We know how dangerous the Welsh backs are. They have a good team with so much talent and I think they will surprise a lot of people at the World Cup.
"I think Wales will get to the quarter-final and I wouldn't be surprised if they can go beyond that."
Contepomi also backed Wales prodigy James Hook to be a leading player on the world stage for the next decade.
Hook's tactical kicking was not at its best on Saturday but he impressed again with the ball in hand and made a scything break to set up Thomas' try.
Contepomi said: "James Hook is one of those players you don't see very often. He will be one of the best - if not the best - outside-halves in the next 10 years.
"He can run himself, he can tackle, he can kick and put people into gaps. He has everything."
Wales regroup on Monday to begin preparations for their final World Cup warm-up outing against a buoyant French side in Cardiff next Sunday.
France arrive on the back of successive wins over England but Martin Williams is confident Wales can build on their performance from the Argentina game.
"If we can keep improving, we can do well in the World Cup. We've had a lot of belief in the camp that the longer we go on, the better we'll get," said Williams.
"Hopefully this has taken us a step forward and will give us more belief. A win always relieves the pressure.
"We have a massive game next Sunday against France, one of the World Cup favourites, and we need to perform."