The Pumas secured a date with the Springboks next Sunday by clinching a narrow 19-13 win over Scotland in a last-eight battle of attrition at the Stade de France on Sunday night.
They continue a relentless pursuit of glory in a World Cup they are taking by storm, and remain unbeaten heading into the semis.
The South Americans have already made history by getting this far, but they will have to rewrite the record books if they are to make the final as they have not beaten South Africa in Test rugby in 11 attempts.
Contepomi knows it will be tough, but is not discounting his men springing yet another surprise.
“We are still taking it game by game,” said the Leinster fly-half, who is playing at centre for the Pumas in the World Cup.
“We are now playing South Africa, statistically one of the superpowers, and we know we are the underdogs.
“We have never beaten South Africa, but who knows? We could do it in the semi-final of the World Cup. That would be magnificent.
“I saw them against Fiji (in their quarter-final). They are physical, have good individuals and have the ability to play different types of rugby.
“Worst of all, their coach Jake White is good friends with our coach and they know each other and our teams well.
“That could make it hard but it’s a great opportunity for us.”
Contepomi and his team-mates are still coming to terms with their achievements over the past month.
They have won five from five, and after topping a testing Pool D that included France and Ireland, they then saw off another of the northern hemisphere’s heavyweights in Scotland.
Their country is going rugby crazy, with even football — the nation’s principal sport — taking a back seat.
The “superclasico” derby between River Plate and Boca Juniors — arguably world soccer’s biggest match — was rescheduled so it did not clash with Argentina’s World Cup quarter-final.
And Contepomi is still pinching himself, adding: “Nobody would have believed this.
“Argentinian people are patriotic and nationalistic, and like to see their teams play with heart and passion.
“In terms of this World Cup, even football people are talking about rugby.
“It is something that a few years ago, we would not have even dreamt about.”
Contepomi has had a fabulous tournament with the boot, and he added 11 points on Sunday to take his campaign tally to 64.
The Pumas handled the pressure well in the tournament’s opening game when they shocked the French 17-12 at the Stade de France.
Sunday night was a different kind of test against an altogether different type of opposition, and Contepomi was relieved to get past the plucky Scots.
“This time, we were the favourites,” he said.
“We had nothing to lose against France, the same as the Scots here. We are not used to being favourites but we assumed the responsibility and we played as best as we can.
“You mustn’t forget that Scotland are a very technical and tactical team, and they deserve credit for not allowing us to play well.”