Juan Cuadrado gave Colombia the lead just before half-time, Neymar levelled in the second half but was left red-faced after sending his penalty kick flying several metres over the crossbar in the 80th minute with a complete mis-kick.
In doing so, he denied Brazil their seventh successive win in a match played at a breakneck pace.
Colombia striker Radamel Falcao, like Neymar one of the world's most sought-after players, had a quiet game, although it was another impressive performance from his side who have flourished under the leadership of Argentine Jose Pekerman.
The Brazilian Football Confederation (CBF) claimed the match was the 1,000th played by their team, although it did not provide a complete list of games which caused confusion about the criteria used.
However, it was clear that the tally included non-international matches as the CBF said the first game was against English club side Exeter City in 1914, when the Brazil team consisted only of players from Sao Paulo and Rio de Janeiro.
Colombia began aggressively, pressing the Brazilian defence in their own half and making it difficult for them to play their way out of the defence. They got into several dangerous positions without creating any clearcut chances.
Brazil had the first opening when Neymar got away to meet Daniel Alves's cross but his effort went straight at goalkeeper David Ospina, who managed to block it from six metres.
Kaka hit the crossbar and Neymar fired over in a brief period of Brazilian dominance before Colombia went ahead one minute before the break.
After a long period of possession, James Rodriguez set Cuadrado clear on the right and the Fiorentina player scored with a low shot into the far corner which Diego Alves got a hand to but could not stop.
Neymar pulled an equaliser out of the hat in the 64th minute as he broke down the left, looking as if he would go outside his marker, but then dragged the ball back and shot between two defenders into the far corner.
Falcao nearly got on the scoresheet two minutes later with a diving header which was brilliantly saved by Diego Alves, who also did well to stop a James Rodriguez shortly afterwards.
Neymar, who has 17 goals in 26 internationals, curled a free-kick centimetres wide before nearly sending the ball out of the stadium with his duffed penalty.
The miss could be considered poetic justice for Colombia's players who protested long and hard over the penalty, urging the referee to look at the replay on the stadium screen, after Daniel Alves went theatrically to ground.
