Jhon Murillo gave the visitors the lead with a close-range finish but a second-half own goal earned Argentina a point.
They are fifth in the South American standings with two games remaining and the top four qualifying automatically – the fifth-placed team faces a two-leg play-off against New Zealand.
Brazil, who have already qualified, drew 1-1 with Colombia.
Chelsea forward Willian gave Brazil the lead before Monaco striker Radamel Falcao equalised. Liverpool midfielder Philippe Coutinho came off the bench for Brazil late on.
Uruguay moved up to second after beating Paraguay 2-1 while Peru beat Ecuador by the same scoreline to move up to fourth. Sixth-placed Chile lost 1-0 to Bolivia.
Chile, who are one point behind Argentina, host Ecuador before finishing their campaign with a trip to top-of-the table Brazil in next month’s final qualifiers.
Argentina, who have won the tournament twice and were runners-up in 2014, are level on points with Peru, who they host next, before a trip to Ecuador. Peru’s final qualifier is at home to Colombia.