The 24-year-old, fresh off guiding Brazil to gold at the Olympic Games in Rio, netted the match-winner with 16 minutes remaining in Manaus.
Brazil had a dream start after Miranda opened the scoring in the second minute at the Arena da Amazonia.
The Inter defender headed the home side into the lead courtesy of Neymar’s early corner, but Colombia struck back in the first half.
It was not a Colombia player who found the net, however, with Marquinhos putting the ball past his own goalkeeper Alisson from a teasing James Rodriguez cross.
But it was Brazil who came out on top, with Neymar firing home a low strike after being set up by Liverpool attacker Philippe Coutinho.
The win put Brazil up to second in the CONMEBOL standings, equal on points with Argentina and one behind leaders Uruguay after eight games.
Brazil coach Tite went in unchanged from his first game at the helm – a 3-0 win away to Ecuador last Friday.
The Brazilians got off to an ideal start, with Miranda heading in a Neymar cross in just the second minute of the match.
Neymar had the chance to double the lead with a free-kick in the 14th minute but saw his effort sail harmlessly over the bar.