Despite an entertaining first half at MetLife Stadium, the two understrength South American sides were unable to find a breakthrough.
Argentina – without Lionel Messi – were perhaps the better side for the most part, but Colombia also had their chances on Tuesday.
But under interim coaches Lionel Scaloni and Arturo Reyes, the teams played out a draw, leaving Colombia without a win against Argentina since 2007.
Argentina looked the more dangerous side in the opening stages, and Exequiel Palacios forced a good save from David Ospina in the seventh minute.
Scaloni's side continued to search for an opener and Mauro Icardi was the next to be denied by Ospina, who kept out the Inter forward after he was played through by Nicolas Tagliafico.
Argentina were almost punished for those missed chances approaching the half-hour mark, Radamel Falcao's low strike pushed away by Franco Armani.
Colombia grew into the encounter as the half wore on and while it was a mostly open first 45 minutes, the teams headed into the break level.
Armani was needed to keep Argentina level just after half-time, the goalkeeper diving to his left to deny a powerful strike from Luis Muriel.
However, despite both teams pushing for a winner amid a flurry of substitutions, they struggled to create clear-cut chances.
What does it mean: Argentina rebuild appears on track
Even without Messi, there still seems enough to be positive about for Argentina after a last-16 exit at the World Cup. Giovani Lo Celso produced a good performance and Palacios – the 19-year-old making just his second appearance – also looked decent at international level.
Pat on the back: Lively Lo Celso takes responsibility
In Messi's absence, Lo Celso was crucial to Argentina's best attacking moments. The midfielder, who is on loan at Real Betis from Paris Saint-Germain, showed his passing capabilities in helping create his team's best chances.
Boot up the backside: No Messi, Scaloni opts against giving Dybala major chance
While Lo Celso showed good signs, Paulo Dybala was given just 35 minutes across two friendlies. With Messi absent, Argentina had a chance to see what the Juventus star was capable of as their main man, but Scaloni opted against giving Dybala a greater chance to impress.