Argentina goalkeeper Sergio Romero made four saves from the Colombia attack when they had only him to beat, earning the man of the match award as coach Sergio Batista's team were booed off by their own fans at first division Colon's stadium in Santa Fe.
"We don't like [to be booed] but we have to respect the people, who want to see their team win," Batista told the post-match news conference.
The home side also failed to put away chances while Batista's tactics did not help the heavily marked Lionel Messi, who exerted little influence and even blasted a free kick over the top.
The hosts could be pushed into third place in the group if Bolivia, who held the hosts 1-1 in the group opener last week in La Plata, beat Costa Rica in Jujuy on Thursday. Colombia beat the Costa Ricans 1-0 last Saturday.
"Now we must keep our calm because we know we're playing for everything in the next match," Batista said.
The first chance fell to Argentina when full back Pablo Zabaleta came in from the right in the eighth minute and beat goalkeeper Luis Martinez with a low shot that was cleared off the line, denying the hosts a settling early lead.
Ten minutes later, midfielder Esteban Cambiasso crossed from the left and the ball looked on its way in to the top far corner before Martinez tipped it away.
STINGING BREAKS
Colombia, launching stinging counter-attacks whenever Argentina lost the ball, should have gone ahead in the 20th minute but were guilty instead of their first glaring miss.
Winger Dayro Moreno crossed low from the left wing to the unmarked Adrian Ramos but the midfielder contrived to hit the ball over the bar with Romero beaten.
Six minutes later, Ramos leapt onto a poor back pass by Gabriel Milito but was tackled from behind by fellow central defender Nicolas Burdisso.
Brazilian referee Salvio Fagundes played the advantage as the loose ball ran out left to the unmarked Moreno but he shot into the side netting.
"You have to remember that like us, they are trying to settle into [the game] their coach wants," Colombia captain Mario Yepes said of the missed chances for both sides.
"We're happy with how we played but were always wary because Argentina have players who can sting you at any moment."
Messi had one of his few potentially telling moments of the match just past the half hour with a superbly weighted through ball to Ezequiel Lavezzi but the winger delayed his shot just enough for Martinez to block.
Colombia, living up to their billing as dark horses, brought two diving saves from Romero in the final three minutes of the half, first from a swerving shot from outside the box by striker Radamel Falcao and then from Moreno.
Argentina captain Javier Mascherano had a shot saved early in the second half and minutes later Colombia left-back Pablo Armero shot just wide of the far post.
Colombia should have taken the lead in the 67th minute when Argentina wer
