The Colombians made the breakthrough with just five minutes on the clock when Pablo Armero arrived in the box to scuff his shot home from 12 yards.
Greece almost responded instantly, but Panagiotis Kone could only slice his shot wide following a quick break from the former European champions.
Colombia looked the more likely to score as the half drew to a close thanks to some incisive attacking play, but it was Greece who came closest when Kone's rasping drive from the edge of the area was parried away by David Ospina.
The South Americans started the second half in lively fashion, and they were able to double their lead on 57 minutes when Teofilo Gutierrez was on hand to prod in a corner from close range.
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Greece should have had a goal back five minutes later as Theofanis Gekas was afforded plenty of space inside the Colombia box, but the forward somehow hit the crossbar from close range when he looked certain to score.
The Greeks huffed and puffed as time began to run out for them, but they were unable to give themselves a lifeline as Giorgios Samaras curled a good chance wide late on.
Instead, Colombia made sure of the win deep in stoppage time as Rodriguez provided a cool finish into the bottom corner following a dynamic break.