The defeat was Brazil's first in 12 matches and the first game coach Dunga had failed to win since taking over following their disastrous 2014 World Cup.
The scrappy game threw up few clear chances but Colombia put away the one that mattered to get the win over their illustrious rivals and record only their second victory in 10 Copa America encounters against the five-times world champions.
Colombia were the better side throughout with defender Murillo seizing on a loose ball to get the all-important goal nine minutes before half time after a Juan Cuadrado free kick had bobbled around in the box.
Scuffles broke out at the end of the match and Neymar and Bacca were both shown red cards. The Brazilian had already been given a yellow and will miss Brazil's next match against Venezuela and probably at least one more game.
The striker was a different man from the one who turned on the style in previous matches for club and country and his team mates blamed the referee for singling him out.
"Referees need to show Neymar more respect," Willian told television reporters after the game. "He is always being targeted."
Brazil's Roberto Firmino should have equalised 13 minutes into the second half but he skied a golden chance over the bar with the goal gaping.
The result leaves Colombia and Brazil tied at the top of Group C along with Venezuela, who play Peru on Thursday.
(Writing by Andrew Downie; Editing by Peter Rutherford)
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