The tournament hosts are through to a semi-final show-down against Germany after holding-on to win a scrappy contest against their South American rivals.
Brazil captain Thiago Silva gave his side the perfect start when he scored after just 7 minutes.
And a thunderous 35-yard free-kick by David Luiz mid-way through the second-half appeared to have sealed a comfortable victory.
But the Colombians set-up a tense finish to the game when their star, James (pr: Hamez) Rodriguez converted an 80th minute penalty as Brazil were left hanging-on for a narrow win.
Earlier, Germany booked their place in the semi-finals with a 1-0 win over a surprisingly subdued France in the Maracana.
A first-half header from centre-back Mats Hummels was enough for the three-time champions to advance to a final-four show-down with the tournament hosts on Tuesday night.