Already assured of progress, Colombia went ahead with a 17th-minute Juan Cuadrado penalty, only for Shinji Okazaki to equalise with a diving header before the break as Japan sought the win they needed to have any chance of progressing.
Martinez restored Colombia's lead with a sharp strike after 55 minutes and then produced a cool finish to make it 3-1 eight minutes from time before James Rodriguez added a delightful fourth goal with a clever run and chip over the keeper.
Colombia, who are in the last 16 for the first time since 1990, finished on nine points with Greece going through in second place to face Costa Rica after their 2-1 win over the Ivory Coast. Japan were bottom with one point.
(Reporting by Mitch Phillips, editing by Ken Ferris)
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