The Liverpool No.10, who has six for his club this season, broke the deadlock in the 25th minute in Belo Horizonte with a trademark long-range effort.
After cutting in from the left hand side, Coutinho drove past his markers and lashed a fierce finish into the top corner from outside the area.
Further goals from Neymar and Paulinho ensured a fifth consecutive win for Tite’s team, who now lead the South American standings by one point.
Reds forward Roberto Firmino came on as a substitute on 82 minutes, while Coutinho was taken off with five minutes remaining.