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 on Tuesday 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 added 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.
In Texas, Costa Rica beat Paraguay 2-1 but failed to progress.
Paraguay goalkeeper Rodrigo MorÃnigo is beaten by a Francisco Calvo header. (AP PHOTO)
Costa Rica (four points) needed results to go their way along with a big swing in goal difference to qualify and they wasted no time getting on the board when skipper Francisco Calvo and Josimar Alcocer made it 2-0 inside seven minutes.
But their hopes of moving on dwindled 10 minutes into the second half when Mathias Villasanti dribbled into the box and set up Ramon Sosa, who blasted the ball into the top corner for his first goal for Paraguay (zero points).
COPA AMERICA QUARTER-FINAL DRAW
* July 4 - Argentina v Ecuador (Houston, Texas)
* July 5 - Venezuela v Canada (Arlington, Texas)
* July 6 - Colombia v Panama (Glendale, Arizona)
* July 6 - Uruguay v Brazil (Paradise, Nevada).
6°C