Colombia also qualified for the Round of 16 for the first time since 1990 when they had lost 1-2 to Cameroon in the second round.
Colombia's first goal came in the 17th minute when Portuguese referee Pedro Proenca gifted them a penalty after Yasuyuki Konna brought down Adrian Ramos in the penalty area. Juan Cuadrado scored from the spot kick to put the South Americans 1-0 ahead.
FINAL GROUP C STANDINGS
Colombia Played 3, Won 3, Goals for 9, Goals against 2, Points 9
Greece Played 3, Won 1, Lost 1, Drawn 1, GF 2, GA 4, Points 4
Ivory Coast Played 3, Won 1, Lost 2, GF 4, GA 5, Points 3
Japan Played 3, Drawn 1, Lost 2, GF 2, GA 6, Points 1
Japan then had a series of attacks on the Colombian defence but couldn't convert till the added time in the first half when Shinji Okazaki's diving header brought the Asians back into the game.
Japan, who had started well in the tournament, bowed out with just one point
But it was all Colombia after the interval. Substitute Rodriguez found Jackson Martinez on the edge of the penalty area and the latter powered home a low-angle kick in the 55th minute. Japan made some valiant efforts during this period to draw level but Martinez's second of the match in the 82nd minute and Rodriguez's third of the tournament in the 90th minute sealed the match's fate.
The Colombia-Japan match made a history when 43-year-old Farid Mondragan beat Cameroon's Roger Milla's record as the oldest player at the World Cup finals. The goalkeeper came on as a substitute for the last six minutes and made a nice save.