The Monaco forward has been outstanding throughout the tournament in Brazil and he again showed his star quality with a strike fit to grace the iconic Maracana on Saturday, as he put together a virtuoso performance to send his side through to a last-eight meeting with hosts Brazil.
His unstoppable long-distance 28th-minute volley will no doubt be considered as one of the best goals in World Cup history, and when the 22-year-old followed up by netting a second five minutes after the break he added gloss to his own display.
That first sensational strike helped to ensure the encounter will be remembered for all the right seasons, with the pre-match build-up having been marred by the fallout from Luis Suarez's four-month ban from any football activity for his alleged bite on Italy's Giorgio Chiellini in the group phase.
Suarez - who was also hit with a nine-match international suspension - has protested his innocence with Uruguay having appealed FIFA's ruling, but in his absence Oscar Tabarez's men struggled to find any real penetration going forward.
Indeed, Uruguay started on the defensive and it took James Rodriguez's strike to light up the encounter.
Colombia dominated possession in a nervy opening, although they were mainly limited to shots from distance.
Uruguay appeared content to sit deep and initially seemed to be doing a good job of stemming the threat of the Monaco forward, who took time to put his stamp on the match.
But when his arrival into the thick of the action came, it was spectacular to say the least.
A bout of head tennis seemingly left Uruguay in little danger, until the youngster - poised on the edge of the area - controlled the ball on his chest 30 yards from goal before he swivelled on the spot and unleashed a ferocious left-footed volley that crashed in off the underside of the crossbar - via the faintest of touches from goalkeeper Fernando Muslera.
Stunned into action - with the rest of the stadium still taking in that wonder strike - Uruguay sought a swift response and Edinson Cavani found space on the left before his teasing cross was headed away by Carlos Sanchez with Cristian Rodriguez ready to pounce.
Shortly afterwards, David Ospina made a smart save from Alvaro Gonzalez's rasping shot.
Despite the improvement, Uruguay's task became even more difficult in the 50th minute as James Rodriguez doubled his tally.
Colombia worked the ball from right to left and Pablo Armero put in a wonderful cross to the back post, where Juan Cuadrado unselfishly nodded the ball down and back into the path of James Rodriguez, who swept home from close range.
Uruguay desperately needed a quick goal and Cristian Rodriguez forced a fine stop from Ospina with an accurate left-footed shot that would have found the top corner but for the goalkeeper's intervention, before Cavani flicked a header just over the crossbar in the 70th minute.
The Paris Saint-Germain forward went close again with a low-angled drive late on but Uruguay's pressure was comfortably soaked up.With five minutes left, Adrian Ramos replaced James Rodriguez. He left the pitch to a raucous reception from the Colombia's supporters - who were soon able to celebrate a place in the World Cup quarter-finals for the first time.