The striker shot a powerful volley to the right side of goalkeeper Weverton and scored possibly the best goal of the tournament.
Colombia then started defending against a Brazil team that barely stopped surrounding its penalty box. It appeared as if Colombia would be able to hold out, until Argentine referee Nestor Pitana's knee came into play. Pitana accidentally blocked a pass by Neymar about 10 meters in front of the Colombian area in the 78th minute.
Colombian defenders momentarily stopped, but Brazil substitute Lucas Paqueta just moved the ball to left-back Renan Lodi and his cross found Roberto Firmino, whose angled header beat Colombian goalkeeper David Ospina.
The Colombians initially refused to restart the match but Pitana, the referee of the 2018 World Cup final, confirmed Brazil's goal.
Brazil kept pressuring in the final minutes and found its reward in added time. Neymar took a corner and Casemiro netted the winner.
"They came at us once and then stopped,'' Casemiro said after the match. "It was our attack against their defense. Colombia is a strong team but, as the coach requires, we are very strong mentally.''
On Thursday, the Colombian football federation asked Copa America organisers to suspend Pitana, saying he prejudiced the result by not halting play in the lead-up to Firmino's goal.
Brazil leads the group with nine points after three matches. Colombia has four from four matches. Peru also totals four points followed by Ecuador (3) and Venezuela (2). The top four teams advance to the playoff stage. Brazil will play its last group stage match on Sunday against Ecuador.