The pre-match build-up had been dominated by talk of Suarez's four-month ban for biting Italy's Giorgio Chiellini, but by the final whistle at Rio de Janeiro's Maracana, there was only one name on everyone's lips.
Having previously illuminated the group phase, Rodriguez broke the deadlock shortly before the half hour with a breath-taking strike, chesting the ball down and volleying home from 25 yards.
The 22-year-old Monaco playmaker added a second early in the second half, sending him to the top of the scorers chart with five goals and confirming his emergence as one of the players of the tournament.
His goals took Colombia into the quarter-finals for the first time, meaning the northern Brazilian city of Fortaleza will turn completely yellow when Jose Pekerman's side play the hosts on July 4.
Uruguay's fans sported Suarez masks and brandished banners in support of their wayward star, who flew home to Montevideo on Friday, while his shirt was hung up in the Uruguay changing room.
But they were to endure a night of disappointment on their return to the Maracana, scene of the country's seismic 2-1 win over Brazil in the deciding game of the 1950 World Cup.
Diego Forlan replaced Suarez for Uruguay, while Colombia coach Pekerman sprang a surprise by selecting two centre-forwards in Jackson Martinez and Teofilo Gutierrez.
Although Martinez lined up on the left flank, there was no lack of ambition to Colombia's play.
Juan Cuadrado and Juan Zuniga set the tone with purposeful early runs at the Uruguay defence, with one of the latter's raids culminating in a low shot that Fernando Muslera gathered at the second attempt.
Uruguay were content to cede possession to their opponents, sitting deep on the edge of their own box, but their defences were breached in the 28th minute by a goal of jaw-dropping splendour.
After Abel Aguilar saw a chipped pass cleared back to him, he headed the ball up to Rodriguez, who was standing just outside the penalty area.
The Colombia number 10 controlled the ball on his chest, turned, and unleashed a magnificent dipping volley that crashed in off the crossbar.
Rodriguez, who has now scored in each of his last six international games, celebrated with appropriate abandon, screaming 'Vamos!' at the hordes of jubilant yellow-shirted fans in the front-row seats.
Uruguay set about trying to wipe out the deficit, but Edinson Cavani's free-kick narrowly cleared the bar and Alvaro Gonzalez was foiled by a full-length parry from Colombia goalkeeper David Ospina.
Colombia doubled their lead five minutes into the second half with a fine team goal.
Pablo Armero's deep left-wing cross was headed down by Cuadrado and Rodriguez swept home his second of the night from close range.
Ospina kept Uruguay at bay thereafter, parrying shots from Gonzalez, Cristian Rodriguez and Cavani and saving bravely from Maxi Pereira.
Uruguay's frustration began to tell, with substitute Gaston Ramirez booked for a wild kick at Armero.
Four years after reaching the semi-finals in South Africa, Uruguay's World Cup ended at the scene of their greatest triumph.
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