Colombia, who finished top of Group D on seven points, face Panama in the quarters while second-placed Brazil take on Group C winners Uruguay.
A frantic first fifteen minutes at Levi's Stadium saw Colombia go within inches of scoring after James Rodriguez hit the crossbar, before Raphinha whipped a sublime free kick into the top corner to give Brazil the lead in the 12th minute.
Colombia had a Davinson Sanchez goal disallowed for offside before striker Jhon Cordoba's brilliant through ball was rifled into the net by Daniel Munoz to level the scores in first-half stoppage time.
Despite the searing California heat neither side let the intensity drop after the break. Raphinha fired a free kick just wide and Andreas Pereira tested Camilo Vargas with a long-range effort but Colombia held on for the draw and stretched their unbeaten run to 26 matches.