Thiago Silva's seventh-minute goal has put Brazil on course for a spot in the semi-finals of the World Cup.
The tournament hosts were ahead early on courtesy of their captain, who bundled the ball home at the back post unmarked from Neymar's corner.
Colombia nearly hit an instant reply through Juan Cuadrado's drilled effort, but a deflection off Silva on the way through ensured that the strike did not trouble Julio Cesar.
Three chances in short succession followed for Brazil as Hulk's cut-back was just about dealt with after he initially beat a man inside the area, before seeing another shot kept out by David Ospina who did well to get up to keep out the rebound.
Ospina was called into action again on the 28-minute mark to deny Hulk once more, as the much-maligned wideman latched on to Marcelo's cut-back inside the area before getting a shot away.
Neymar tried his luck from a free kick just before the interval, only for his attempt to fly high of the target with Ospina rooted to the spot.
