The South Americans, who last qualified in 1998, went ahead early through Pablo Armero and their lead was doubled just before the hour mark by Teofilo Gutierrez.
James Rodriguez sealed the win by placing the ball in from the edge of the box in stoppage time.
Greece created several chances, and went close just after Colombia’s second when Theofanis Gekas hit the bar with a diving header.
The result gives Colombia a great chance of making the last 16 for only the second time, from a group containing Japan and Ivory Coast, who they play next.
But Greece face a difficult task and will rue the fact that they did not take their chances when they came in what was, at times, an entertaining start to Group C’s fixtures.
The game at the Estadio Mineirao had barely settled down when Colombia took the lead through the unlikely source of the Napoli left-back who played five times while on loan at West Ham last season.
Juan Cuadrado pulled the ball back from the right to find Armero in a central position on the edge of the box, and his shot bobbled past Greece goalkeeper Orestis Karnezis following a wicked deflection off Kostas Manolas….
South Africa Today Sport – Football News – Colombia vs Greece – Football