A free kick by Barcelona star and national captain Neymar and a late goal by Luan saw the home side reach the semi-final stage
Brazil have never won Olympic gold at football but both the men's and women's sides have reached the semi-final stage of Rio 2016.
A low, pinpoint shot past Colombia goalkeeper Cristian Bonilla) from a free kick by Brazil captain Neymar – the first goal of the tournament for the Barcelona star – opened the scoring for the host nation in the 12th minute.
Luan added a second in the 82nd-minute when he cleverly lobbed the ball over Bonilla from outside the box.
It was the home side who always looked stronger and most likely to score.
Neymar, who played despite an ankle sprain, dominated the action and was a constant target for Colombia's defence.
In one, nine-minute period during the first half, three Colombian players received yellow cards, each after rough tackles on the Brazil star.
The frustrated striker received a yellow card of his own on 40 minutes after a rough tackle on Andres Roa, which sparked some tense moments between the teams.
Colombia's best chance came just before the hour, when Miguel BorjaL) fired a rocket that was well saved by goalkeeper Weverton of the home side.
Colombia enjoyed better possession in the second half but Brazil were able to develop enough counter attacks to force a second goal, much to the relief of the boisterous 41,560 crowd.
In their semifinal on Wednesday (17 August) in the Maracanã in Rio de Janeiro, Brazil will face surprise package Honduras, who defeated Republic of Korea 1-0 on Saturday at the Mineirão stadium in Belo Horizonte.
In the other semi-final, Germany will take on Nigeria.