The Monaco attacking midfielder scored with an outstanding 22-yard volley after 28 minutes of the round-of-16 clash at the Maracana, and then swept home a second from close range after five minutes of the second half to take charge of the race for the Golden Boot with five goals.
Uruguay, without the banned Luis Suarez, fought hard in an attempt to find a route back into the game after the break but Colombia - and particularly their goalkeeper David Ospina - held firm to book another all South American encounter with hosts Brazil in Fortaleza next Friday night.
Uruguay coach Oscar Tabarez made two changes to the team that beat Italy 1-0 in their final Group D clash, with Maxi Pereira and Diego Forlan replacing Nicolas Lodeiro and Suarez. Initially, they broke up the game in Rio with some muscular tackling - often just over the line of legality.
Colombia showed seven changes from the side that began the 4-1 win over Japan, as Jose Pekerman brought back his best players. Juan Zuniga did break forward on a lung-busting run early on but his shot was too straight, into the chest of Uruguay keeper Fernando Muslera.
Then came Rodriguez's special moment - and the World Cup is unlikely to see a better goal. Having maneouvred himself into space centrally, he took Abel Aguilar's header on his chest 22 yards out and then volleyed a shot left-footed over Muslera's fingertips, with the ball bouncing down in off the bar.
After that, Uruguay began to show more ambition. Edinson Cavani put in a dangerous cross that Carlos Sanchez just cleared, then the Paris Saint-Germain striker struck a fierce free-kick that sailed just over the bar.
Buoyed by that, Uruguay ended the half on the up. Their own Rodriguez, Atletico Madrid midfielder Cristian, tried his own volley but Ospina parried it away desperately.
The decisive second goal arrived on 50 minutes, and this time it was a tremendous team effort. Teo Gutierrez started the move on the right before play was spread to Pablo Armero on the opposite flank. His deep cross was headed back and down by Juan Cuadrado to the edge of the six-yard box where Rodriguez was lurking to score once more.
It was looking desperate for Uruguay, even more so when Cristian Rodriguez was again denied by the unbeatable Ospina after hitting a low, raking drive from 25 yards.
Cavani then found substitute Christian Stuani with a wicked delivery to the back post but the substitute striker's header was wide. It was the sort of chance that Suarez would have snapped up.
Maxi Pereira nearly bundled his way through to score, but Ospina came charging out to block.
Colombia now face the toughest of tasks, against the hosts at the Estadio Castelao. It will be James Rodriguez - who was given a standing ovation when he was substituted with four minutes left - against Neymar, and on this evidence we are in for a treat.
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