Victory was sweet for Colombia, who were subjected to rough-house tactics from Brazil last year during the World Cup in a 2-1 quarter-final exit, a match scarred by a whopping 54 fouls.
A pulsating opening 45 minutes saw Colombia gradually get on top after a frantic start dominated by defence.
Brazil, who brought in Thiago Silva at centre-back in place of David Luiz, defended in depth throughout, dropping back in numbers and frustrating Colombia's attack.
Colombia also gave no quarter, with defensive midfielder Carlos Sanchez breaking up Brazil's attacks in midfield and restricting the five-time world champions to hardly any shots on goal.
Colombia slowly began to get the better of their opponents, however, and soon started to threaten.
A Sanchez shot deflected just wide of Brazilian defender Miranda just after the half-hour mark and then on 36 minutes the breakthrough came.
Cuadrado's teasing free-kick from the right flank dropped into the area and when Brazil failed to clear, Murillo was on hand to rifle in a low shot past Jefferson.
Chelsea star Cuadrado might have doubled Colombia's lead on 43 minutes but wastefully shot wide after being teed up by Teo Gutierrez's deft backheel.
Brazil might have grabbed a barely deserved equaliser just before half-time though when Dani Alves skipped clear down the right and curled a cross into Neymar whose diving header was saved by David Ospina.
Neymar was booked for handling the rebound from Ospina's save.
Brazil went for broke in the second half, bringing on Liverpool attacking midfielder Philippe Coutinho for Fred, and immediately looked more threatening as a result.
But they squandered a golden chance to equalise on 58 minutes when Bundesliga-based striker Roberto Firmino missed an open goal.
The ball ended up with Firmino after Ospina made a hash of a clearance. But with an open goal begging, Firmino - reportedly a summer transfer target for Liverpool - blasted over the bar.
-AAP
