Tipped by some to exit against a side who have been the talk of the tournament, Luiz Felipe Scolari's men progressed thanks to goals from Thiago Silva and David Luiz in Fortaleza, the latter a superb 25-yard free-kick.
Man-of-the-moment James Rodriguez pulled one back from the spot for Colombia in the 80th minute, yet Brazil held on to book a semi-final meeting with Germany.
Silva picked up a needless yellow card in the second period, while Neymar was carried off on a stretcher late on to put a dark cloud over Brazil's win.
The duo's potential absences, combined with another workmanlike showing, will do little to dispel claims from the likes of Diego Maradona that Brazil are not good enough to win the tournament.
Much had been made of Brazil's perceived mental frailties ahead of the match, with players coming under fire for crying during renditions of the national anthem and Scolari's decision to call in a sports psychologist grabbing headlines.
Silva was the hero, sneaking behind Carlos Sanchez and kneeing home at the back post from close range after Colombia fatally failed to clear Neymar's corner.
Behind for the first time in the competition, Colombia found an immediate response as Juan Cuadrado's effort was deflected just wide.
Colombia wasted a Rodriguez-led four-on-two counter-attack in between those saves, with the game's end-to-end nature making for a thrilling spectacle.
The second period did not assume the same pace, Jose Pekerman's side failing to find the fluency that has been their calling card.
Rodriguez, so often Colombia's star, crucially brought down Hulk 25 yards from goal, paving the way for Luiz to send a stunning curler beyond Ospina.
The goalkeeper was fortunate not to be shown a red, although that had little impact on tournament top-scorer Rodriguez - who continued his record of scoring in every game when he coolly sent Cesar the wrong way.
The departure of their talisman did not stop his team-mates from defending outstandingly, although Brazil's win came at a cost.
