The Colombians had lost their first group match to Venezuela, and knew that a second loss would all but destroy their chances of qualifying.
Jeison Murillo had gotten the only goal of the game following a goal mouth scramble in the 36th minute.
Colombia kept Brazil at the bay for the rest of the game, frustrating their opponents to record their first win over them in 24 years.
Carlos Bacca had retaliated with a shove, which also got him sent off.
Watch highlights of the game below.