Rodriguez scored in each half as Colombia accounted for South American rivals Uruguay 2-0 in their round of 16 clash at the Maracana on Saturday.
The pick of the bunch was Rodriguez's 28th-minute opener in Rio de Janeiro, which will go down as one of the greatest goals in World Cup history after controlling the ball on his chest before swivelling and unleashing from 30-yards out.
Speaking post-game, the 22-year-old attacking midfielder - the tournament's leading scorer with five goals in four games - could not contain his delight after scoring at the iconic stadium.
"It's historic, a dream come true," said Rodriguez, who has now scored seven goals in his past six international games.
"I always wanted to score in the Maracana and now I have.
Colombia's win over Uruguay set up a last-eight showdown with host nation Brazil in Fortaleza on Friday.
And although Rodriguez acknowledges the task ahead, the Monaco star is confident his side can advance deep into the showpiece event.
"Uruguay had a lot of men behind the ball, so we needed plenty of movement up front and we got it," he said.
"If you want to win, every player is important.
"Now things are going to get even harder but we can go far."
Colombia coach Jose Pekerman was full of praise following Rodriguez's match-winning performance, especially in the absence of injured striker Radamel Falcao.
"The main factor (in this win) was the first half, when we were very solid and managed to get ahead," he said.
"It's great to have a player like James Rodriguez and his confidence was very high after our previous game."
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