Miranda gave the hosts the lead in the second minute before Colombia equalized through a Marquinhos own goal.
The victory was Brazil’s second in as many matches under new manager Tite, who replaced Dunga after the Selecao’s group-stage elimination from the Copa America in June.
The five-time World Cup winners now have 15 points from eight matches, just one point behind leaders Uruguay.
Colombia were put on the back foot immediately in stifling conditions at Arena Amazonia. The opening goal came via a pinpoint Neymar corner that Miranda met with a powerful header at the near post.
While Tite has helped Brazil to rediscover their old attacking self, there are still question marks over the Selecao’s defence.
They were made to look all at sea in the 36th minute when Marquinhos clumsily nodded a curling James Rodriguez free-kick into his own net.
Just like he did against Ecuador in Quito on Thursday, Philippe Coutinho made an immediate impact after being introduced as a second-half replacement for Willian.
The Liverpool No. 10 orchestrated Brazil’s winner by starting a move that also included Gabriel Jesus and then releasing Neymar with a deft through ball from the top of the box.
The Barcelona star needed only one touch before rifling an unstoppable shot past goalkeeper David Ospina.
Coutinho should have scored a goal of his own when he found himself in space minutes later, only to take a moment too long and allow his shot to be partially blocked.
In Montevideo, Paris Saint-Germain striker Edinson Cavani scored twice as Uruguay routed Paraguay 4-0. Luis Suarez and Cristian Rodriguez were also on target for the Celeste.
Lucas Pratto and Nicolas Otamendi netted second-half goals as Argentina – who were without injured captain Lionel Messi – recovered from two goals down to draw with Venezuela in Merida. Josef Martinez and Juanpi scored for the hosts.
And in Santiago, Copa America champions Chile were held to a surprise goalless draw by Bolivia.