Neymar headed in a fifth-minute equaliser before creating a goal for team-mate Douglas Costa deep into stoppage time to seal Brazil's 11th consecutive victory since last year's World Cup.
"This is a very tough competition," Neymar said afterwards as he collected a man-of-the-match award. "We got the win and that's important."
Neymar has now reached 44 international goals at the age of 23, a year earlier than Brazilian legend Pele.
The Brazilian star was at the centre of the action throughout the game, even getting a bizarre yellow card for pushing aside the foam the referee had sprayed on the pitch to show where a free kick should be taken.
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Brazil coach Dunga praised the contribution of his captain.
"Neymar was again decisive," Dunga said afterwards. "He's played three finals in Spain (with Barcelona), and he's had a long season. But he comes here and takes responsibility for sorting out our problems."
- Last Gasp -
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But with the final whistle looming, Neymar advanced menacingly down the left flank and threaded a pass through a forest of bodies for unmarked Shakhtar Donetsk striker Douglas Costa.
Douglas, who had earlier squandered a golden chance created by Neymar, made no mistake with his second opportunity, calmly placing his shot beyond the despairing dive of Pedro Gallese.
While Brazil can now start planning for the knockout rounds, Group C rivals Colombia must regroup after their upset defeat to Venezuela.