Rodriguez made it two for the night and five for the tournament shortly after the restart with a more routine strike, tapping home from close range to finish off a good team move.
Here, Sports Mole takes an in-depth look at a momentous night in the history of Colombian football.
On target: 4
On target: 4
Was the result fair?
Absolutely. Uruguay came into the match with a plan to frustrate Colombia and not give their dangerous attackers any room behind to utilise their pace. They showed very little attacking intent before going behind, instead choosing to defend in numbers and leaving their back line very deep.
It looked like it may take something special to change that game plan, and that is exactly what Rodriguez provided with his goal. However, even when they had no choice but to look for an equaliser, Uruguay didn't really threaten the Colombian defence, with David Ospina rarely being called into action.
The stats may say that Uruguay had more shots than their South American rivals, but it wasn't until the 79th minute that they can say they had a clear chance. Colombia didn't create a great deal more in terms of goalmouth action, but they at least tried to play fluid football and looked more capable of scoring throughout. There is no doubting Colombia deserved the win.
It was not the best that they have performed at this World Cup, but in a way that will please Jose Pekerman. His side comfortably saw off the reigning Copa America champions without being at their best, and they still have a few more gears to move through as the tournament progresses.
They could well need those extra gears against Brazil in the quarter-finals, but they will go into that match full of confidence following their fifth straight win. It looked like they may struggle to break Uruguay down today, but when they have a player like Rodriguez on form then he is capable of coming up with the moment of magic needed to counteract defensive tactics.
Aside from the goals it must be said that Colombia didn't really create much today, with their only gilt-edged chance coming with Rodriguez's second. His first wouldn't exactly be counted as a chance as it was such a tough one to score from, but again his quality came to the fore. They will need to improve if they harbour any hopes of going all the way in this World Cup, but it will take a very good team to knock them out.
It is fair to say that they didn't have an ideal build-up to this match, with Luis Suarez's latest indiscretion dominating the headlines. Uruguay made it clear that they felt FIFA had victimised Suarez and, by association, them, but any hope of a backlash on the field never came to fruition.
They may have entered the match with a siege mentality, and they began it like they expected to be under siege for the full 90 minutes. They had at least 10 men behind the ball on numerous occasions when Colombia were in possession, while the back three did not stray from their set positions and remained very deep until the opening goal.
What will anger the fans is that they looked short of ideas, ingenuity and quality without Suarez in the team. Their attacks were laboured and predictable, and they didn't look like scoring until late in the second half when Colombia began inviting the pressure. They came into this match as underdogs, but they will still be upset at having been knocked out with a whimper.
Sports Mole's man of the match
James Rodriguez: While more familiar names such as Arjen Robben, Lionel Messi and Neymar have all lit up the tournament for their respective sides so far, James Rodriguez has arguably been the biggest breakout star of the 2014 World Cup and is a real contender for both the Golden Boot and the Golden Ball.
He was the match-winner today with both goals, the first of which could well end up being goal of the tournament. He has taken on the mantle of the team's star player in the absence of Radamel Falcao and is flourishing with it. His second goal was a simpler finish, but he was once again in the right place at the right time to end a slick team move.
He now has five goals to his name in this tournament, more than any other player and the same tally that won the Golden Boot four years ago. Rodriguez will have to be top of the list of players for Brazil to stop if they are to beat Colombia.
Little to choose from in this regard, with perhaps the biggest 'gaffe' coming when Pablo Armero poked the ball away from Gaston Ramirez when he was about to take a quick free kick, resulting in the Colombian taking a clattering from the Southampton man.
Bjorn Kuipers was a little lenient on occasions today, but that was probably a wise decision in a game that was always going to be feisty. It was bubbling under the surface on a couple of occasions, but Kuipers dealt with it well and kept control.
Colombia: Next up for Colombia is uncharted territory - a World Cup quarter-final. Not just any World Cup quarter-final either as they face hosts Brazil in Fortaleza for a place in the last four.
Uruguay: Uruguay's next scheduled match sees them take on Saudi Arabia in October.