The hosts surged ahead in the seventh minute when they were awarded a penalty. Kevin Gomis brought down Pierre-Emerick Aubameyang inside the Nice area, and the Gabon international himself stepped up to convert the spot kick.
Renaud Cohade fired a shot from outside the area four minutes later, but failed to keep it on target.
Things went from bad to worse for Nice on 24 minutes when Valentin Eysseric was shown a straight red card for a bad challenge.
The pattern continued in the second half, as Fabien Lemoine shot just wide from inside the Nice area on 51 minutes.
Aubameyang found himself in a good position to double Saint-Etienne's lead three minutes later, but shot wide.
That missed chance did not matter for the hosts in the end, as Brandao turned in from close range following a clever ball from Mollo on the hour mark.
Aubameyang skipped past a series of challenges to set up Mollo for Saint-Etienne's third goal of the evening on 70 minutes, before Brandao headed home Romain Hamouma's cross from close range to make it 4-0.