The game was open and the Selecao were grateful for a good stop from Jefferson to deny Cuadrado, as the winger found space and fired a low shot at goal that nearly found the corner.
In the second half, Neymar played a one-two with Fernandinho to stride into the box but he wasn't able to beat Ospina to hand his side the lead.
Colombia were reduced to 10 men when Cuadrado was sent off for his second bookable offence as he put a forearm to the back of Neymar and the referee produced the red card.
The Selecao nearly took advantage of the sending-off when Oscar found the run of Tardelli who did well to shake the attentions of his marker, but he put his shot wide of the post.
Brazil finally took the lead in the 83rd minute through Neymar as he powered a free kick from outside the box past Ospina into the top corner, leaving the keeper with no chance.
Pekerman's side should have levelled in the last minute when Adrian Ramos lifted a cross to the back post for Radamel Falcao, but the striker somehow put his header over the bar from close range, letting Brazil hold out for the win.