The match made World Cup history when Farid Mondragan beat Roger Milla's record as the oldest player at any finals tournament. The goalkeeper came on as a substitute for the last six minutes at the age of 43 years and three days.
Colombia already had the game sealed.
Disaster struck for Japan after 15 minutes when Yasuyuki Konna chopped down Adrian Ramos in the penalty area.
Portuguese referee Pedro Proenca pointed to the spot and Fiorentina striker Juan Cuadrado confidently fired the kick past Japanese goalkeeper Eiji Kawashima.
Japan had chances.
AC Milan's Keisuke Honda curled a left-footed free kick over the wall but the ball went just wide of the Colombian goal.
German-based striker Shinji Okazaki tried an overhead kick after 35 minutes but his effort went spectacularly high. However, he met with better fortune in time added on in the first-half with a fine diving header.
After 55 minutes, substitute Rodriguez found Martinez in space on the edge of the penalty area and the Porto striker powered a low angled shot into the corner.
Even then, Japan did not give up. Honda fired a powerful long range free kick at Colombia goalkeeper David Ospina. Defender Yasuyuki Konno also beat the Colombia defence with a shot from the edge of the area that Ospina covered.
But Martinez added a second and Rodriguez tormented the Japanese defence before chipping the ball over Kawashima to seal victory. (AFP)
|Colombia`s Juan Cuadrado scores the opening goal from the penalty spot during the group C World Cup soccer match between Japan and Colombia at the Arena Pantanal in Cuiaba, Brazil, Tuesday. (AP)|
|Japan forward Shinji Okazaki, middle, celebrates his goal with Shinji Kagawa, right, past Colombia defender Carlos Valdes during the group C World Cup soccer match between Japan and Colombia at the Arena Pantanal in Cuiaba, Brazil, Tuesday. (AP)|
|Japan`s Keisuke Honda, left, and Colombia`s Carlos Valdes fight for the ball during the group C World Cup soccer match between Japan and Colombia at the Arena Pantanal in Cuiaba, Brazil, Tuesday. (AP)|