Lautaro Martinez's instinctive early finish and a 74th-minute tap-in from substitute Giovani Lo Celso secured a 2-0 quarter-final win over Venezuela at the Maracana, the scene of La Albiceleste's FIFA World Cup final defeat to Germany five years ago.
The best performance Lionel Scaloni's side has managed in the tournament to date secured a meeting with the host in Belo Horizonte next Wednesday (AEST) and Otamendi reflected on its improvement from a poor start to the group stage.
"We knew it would be difficult from the beginning. It took time to take off, we got better," the Manchester City centre-back said.
"Now we are in the semi-finals against an opponent where it is a clasico and we hope it will go in favour of Argentina."
Otamendi came out on top in an absorbing duel with Venezuela striker Salomon Rondon as a previously porous Argentina backline showed signs of finding its feet.
"We knew it was going to be a difficult, hard and very intense match," he said.
"The important thing was to keep discipline, with very strong players like Rondon who hold [the ball up] well.
"We controlled the game very well for most of the time. Maybe from dead balls the opponents had a few chances.
"The goal in the second half gave us a cushion. We were attacking and we knew how to keep organised well. It's a great victory for us."
Otamendi's club team-mate Sergio Aguero, whose shots led to both Argentina goals, was similarly fired up by the prospect of taking on Brazil.
"We will try to do our best, as we have been doing, to work for the shirt," he said.
"Argentina-Brazil is not played every day, especially in a competition like this. It generates a lot of expectation, not only in our country but in the world.
"We knew that this match was not going to be easy but we are happy to have gone to the semi-finals. Little by little we are getting better."