The hosts made a perfect start to the match when Thiago Silva bundled them into the lead with just seven minutes on the clock, while David Luiz joined his defensive partner on the scoresheet an hour later with a stunning free kick.
Colombia fought back against their fellow South Americans and halved the deficit through James Rodriguez's penalty, but that wasn't enough as they went crashing out of the tournament.
Here, Sports Mole takes an in-depth look at whether Brazil were worthy winners of an absorbing match in Fortaleza.
On target: 5
On target: 2
Was the result fair?
Just about, yes. Brazil once again did not exactly look like world beaters, but they created a number of decent openings that they could well have taken advantage of on another day. It was a fairly even encounter in terms of general play, but Colombia struggled to supply the killer pass and Julio Cesar had a fairly quiet game.
The hosts deserved their lead at the break, but they struggled to get into any sort of rhythm in the second half and in the end relied on a moment of magic from Luiz to see them over the line. The emphasis was very much on protecting their lead in the second 45 minutes, and David Ospina didn't have much to do as a result.
Colombia may feel that their superior pressure during the second half should have earned them at least a draw after the 90 minutes, but Brazil defended well and dealt with the dangermen effectively. They are worthy semi-finalists.
It has been said a million times that this Brazil side is a shadow of teams gone by, but such criticism is getting quieter and quieter the closer to the final Luiz Felipe Scolari's men get. Again today they were not completely convincing, but they seem to be able to find a way to win, which is a priceless trait in knockout football.
Germany, Brazil's semi-final opponents, will not have been quaking in their boots watching tonight's performance, but the Selecao do seem to be easing their way in to the tournament and if they continue to improve as it progresses then they could well go all the way.
They could be without Neymar after he was stretchered off in the latter stages of this match, so a lot will depend on how they cope without their star player. However, Scolari will be happy with how his side defended this evening and, if they can do that again against Germany, then they will fancy their chances of making it to the Maracana.
They came into this match as arguably the most impressive team in the tournament so far, but they struggled to show that form for large spells of the match. It was an open and attacking game, but Colombia's dangerous players were rarely afforded room to manoeuvre by the Brazilian defence.
The killer pass was missing on a number of occasions for Jose Pekerman's side, who found themselves in a decent amount of promising positions but failed to work Julio Cesar anywhere near as much as they should have done. They certainly improved in the second half but still struggled to find a way through.
Rodriguez was once again the player who looked most likely to create something for his side, but his display rather summed up Colombia's as a whole - bright moments but largely stifled by Brazil. Colombia as a team have lit up this tournament and it is a shame to see them go, but they can exit Brazil with their heads held high.
Sports Mole's man of the match
Thiago Silva: Defence is not usually the first thought when it comes to Brazilian football, but they protected their lead very well this evening and Silva was right at the forefront of that. He made a number of fine interceptions and blocks to avert danger and really led by example throughout.
He also got the opening goal, taking advantage of some poor marking to bundle home at the back post. It was one he would have expected to score, but he still had a bit to do in order to control his effort into the back of the net.
This one goes to Carlos Sanchez for his marking - or lack thereof - for that opening goal. The midfielder was caught ball-watching as Neymar's cross came in and it was far too easy for Silva to nip in and get the goal, giving Colombia a mountain to climb with less than 10 minutes played.
More than 50 fouls and only four yellow cards gives some idea of how lenient Carlos Velasco was tonight. It is good to see a referee not being too card-happy, but there were times when a caution was deserved and the player got away with it. There were some questions over consistency too, with Rodriguez picking up a yellow for his first challenge and Fernandinho not being booked despite a whole host of fouls.
The biggest decision of the evening was the penalty call, and he got that one spot on. It was a fairly clear penalty, but the referee still had to award it in front of a partisan home crowd. The next decision for him to make was whether to send Cesar off, but Luiz being back there may have just saved the keeper.
Brazil: Germany await the hosts in Belo Horizonte next Tuesday as the two heavyweights go head to head for a place in the final.
Colombia: There are no other fixtures on the horizon for Colombia just yet, so they will turn their attention to getting over the disappointment of elimination.