Before the opener in Salvador, Colombia had a dismal record against Argentina, having failed to beat them in the last 12 years.
But they did not let the past dictate their performance at Fonte Nova Arena, convincingly outplaying the Albiceleste for a 2-0 victory.
The first-half proved unmemorable as neither side had a shot on target, with Lionel Scaloni's men particularly lacking tempo and struggling to get the ball forward in their first competitive fixture since their elimination at last year's World Cup.
Colombia's Roger Martinez broke the deadlock in the 71st minute after picking up a long pass from James Rodriguez, before substitute Duvan Zapara doubled the lead from close range in the 86th minute to secure the deserved victory.
Manager Carlos Queiroz lost Luis Muriel to injury after 15 minutes, making way for the welcome addition of Martinez, but will no doubt be pleased with his competitive debut in charge of the Colombians.
Argentina, meanwhile, the runners-up in 2015 and 2016, will be hoping for more from star man Lionel Messi in their next game against Paraguay on Friday.
Colombia go on to face Qatar, one of the two guest nations at the tournament, on Thursday.
In the night's other game, Venezuela and Peru shared a goalless draw after two goals from Peru were disallowed following VAR reviews.