Jhon Duran equalised with 12 minutes left in the first half when he stroked home following Deiver Machado's cutback in a rare attack for the visitors in the opening 45 minutes.
The Colombians took charge after the interval and Borre struck in the 61st minute, netting from 12 yards out after Daniel Schmidt had blocked Jhon Arias' attempt at goal and the ball had looped up invitingly into the air.
Vargas then denied Japan an equaliser five minutes later with a sprawling save to his left to keep out a goal-bound header from substitute Ayase Ueda.
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