Colombia made it four wins from four games at the tournament when they defeated Uruguay 2-0 in Saturday’s second-round match at the Maracana.
And Rodriguez, 22, continued his sensational form at the World Cup, scoring a goal-of-the-tournament contender to open the scoring and also bagging the second, soon after the break.
The Colombians will now square off against tournament hosts Brazil in Fortaleza on 4 July, the Brazilians having needed penalties to beat Chile.
Rodriguez said: “Obviously, we have to watch Brazil closely.
“They have very good players and they play good football, but they'll have to watch us closely as well.
“There’s no pressure, we have good players and we can be dangerous. I think it's going to be a beautiful match."
Rodriguez was modest about his own performance, adding: “I only want to help the team.
"I'm playing at a good level. We're scoring goals and I'm happy because of that."
Colombia coach Jose Pekerman says Brazil’s struggles against Chile might prove to be to their benefit in the long run.
"Having come through such a difficult match as Brazil did, it always raises the level of confidence,” he said.
"We know the potential that Brazil have and it will be a great match. They are two countries that interpret football in the same way.
“We're playing very well as a team and we're going through a good moment.
“James is scoring important goals, but (Juan) Cuadrado is also playing at a great level, as are the strikers, the wingers, the full-backs. We also have a great goalkeeper (David Ospina).
"But we know the match will be hard and that Brazil have the capacity to cause us problems."