Colombia substitute Borja produced a bullet header in the 94th minute to pinch a share of the spoils after Argentina had raced to a two-goal lead inside the opening eight minutes on Tuesday.
Goals from Cristian Romero and Leandro Paredes appeared to have Lionel Messi's Argentina cruising to victory, but Colombia pulled one back early in the second half via Luis Muriel's penalty.
Borja, who was one of three half-time substitutes for Colombia, produced the decisive late intervention, moving his side to eight points from six games in qualifying.
Argentina remain undefeated but have drawn three of their past four qualifiers, having collected 12 points from six games in total on the roar to Qatar 2022.
Atalanta defender Romero powered home a third-minute header from Rodrigo De Paul's set-piece for the visitors.