With the match at Sun Life Stadium seemingly petering out to a draw after Juan Cuadrado saw red early in the second half, Neymar stepped up and curled a free-kick past Colombia goalkeeper David Ospina in the 83rd minute.
The win gave Dunga a winning start to his second spell in charge of the national team, while the result ended a run of back-to-back defeats for Brazil.
Speaking post-game, Dunga highlighted the performance of the 22-year-old star, who took his international tally to 36 goals from 55 appearances.
"The ball sticks to his feet, he does things with a naturalness that others cannot do," said Dunga.
"The most difficult things seem simple for him, is a naturalness that makes everything look easy."
The fixture in Miami was a repeat of the pair's quarter-final meeting at the World Cup in July, which Brazil won 2-1.
And it was Brazil who emerged victorious again thanks to a helping hand from Cuadrado, who received his marching orders for a second bookable offence just four minutes into the second half.
The victory came at the perfect time for Brazil, having been embarrassed 7-1 by eventual world champions Germany and 3-0 by the Netherlands.
"Playing against a team that has been together for four years, well trained, is always difficult," the 50-year-old Dunga said.
"We were a little scratchy and needed a response.
"It was a game very similar qualification: many faults, garbled but the players behaved well and had many positive points.
"They understood well in practice and repeated it in the game."
