Playing with a man less for 41 minutes after star Juan Cuadrado saw red for a second bookable offence, Colombia appeared on track for an unlikely draw in their international friendly at Sun Life Stadium.
But Neymar stepped up with a delightful free-kick that glanced off the post and past Colombia goalkeeper David Ospina in the 83rd minute as Brazil emerged victorious in a repeat of the pair's quarter-final meeting at the World Cup.
Named Luiz Felipe Scolari's successor following Brazil's embarrassing World Cup campaign, Dunga's return inspired an end to the nation's run of back-to-back defeats.
Brazil went into the match having lost 7-1 to eventual world champions Germany and 3-0 to the Netherlands in their third-place play-off.
Tensions were evidently high after the infamous last-eight meeting at the showpiece event in July, when Neymar suffered a tournament-ending fractured vertebra following a heavy challenge from Juan Camilo Zuniga.
And that strain trickled over to Friday's meeting as there were more yellow cards than shots as Canadian referee Dave Gantar was kept busy during a goalless first half.
A total of five yellow cards were handed out, with Cuadrado, Ramires (celebrating his 50th cap), Luiz Gustavo, Zuniga and Carlos Valdes all cautioned.
But it was a lively end to the half after Brazil had a goal ruled out for offside in the 24th minute.
Brazil broke quickly on the counter-attack in the 32nd minute, with attacking midfielder Willian driving forward in a four-on-two situation.
Willian squared the ball to onrushing Chelsea team-mate Oscar inside the penalty area but he flashed his shot wide of the post.
At the other end, Zuniga fired an audacious effort from outside the box just over the crossbar with seven minutes remaining until the interval.
Colombia came close again to breaking the deadlock after Cuadrado forced Brazil keeper Jefferson to turn his low shot away for a corner in the 41st minute.
Referee Gantar was in the thick of the action four minutes into the second half as the match threatened to boil over when Cuadrado was shown a second yellow for a seemingly soft challenge on Neymar.
Brazil's numerical advantage was obvious and they had another chance to make the breakthrough in the 56th minute after Oscar's nifty back-heel played in Diego Tardelli, whose attempt was blocked for a corner.
The five-time world champions finally found the back of the net thanks to Neymar with seven minutes left to play.
After Brazil were awarded a controversial free-kick for a handball, Neymar curled the ball inside the top corner.
Substitute and new Manchester United signing Radamel Falcao had a golden chance to level proceedings for Colombia in the closing stages but his attempt went over the bar.
