Nice paid the price for the first-half dismissal of Valentin Eysseric as St Etienne continued their push for Champions League football next season with an emphatic win.
St Etienne led early on through Pierre-Emerick Aubameyang's penalty but the game turned on the 23rd-minute dismissal of Eysseric, whose ugly challenge on Jeremy Clement spelled the end of the night for both men.
Nice held out with 10 men until the break only for the floodgates to open in the second half, with Yohan Mollo scoring in between Brandao's brace.
St Etienne remain undefeated in 2013 and climbed into third place after a sixth win in seven, leapfrogging both Nice and Marseille, who are in action tomorrow.
Defeat for Nice snaps a run of four wins and a draw in their last five matches and drops them one place to fifth, two points adrift of today's opponents.
Six minutes had gone when the hosts went in front, Aubameyang sending David Ospina the wrong way from a penalty awarded when Kevin Gomis had hauled down the Gabon striker in the area.
With just one goal conceded in their last four league outings Nice would have fancied their chances of limiting their losses to just the one goal, but that changed midway through the half when Eysseric went in with a nasty tackle on Clement and received a straight red card for his trouble.
Clement was also forced to leave the action with an injury, with Josua Guilavogui his replacement.
The hosts might have punished Nice further before the interval but Ospina was alert to efforts by Renaud Cohade and Mollo.
Nice doubtless feared a second-half onslaught against a side whose league exploits have been supplemented by a run to the final of the Coupe de la Ligue and the last eight of the Coupe de France, and Aubameyang duly served a warning within minutes of a restart with a shot just wide.
But Nice's luck would not hold for much longer, and with an hour gone it was 2-0 as Mollo did the hard work with a fine run and cross for Brandao who had a simple task to fire home.
With 20 minutes remaining the hosts had another as Aubameyang beat three men before crossing for Mollo to turn in from close range, and five minutes later the scoring was complete as Romain Hamouma beat two men before flicking the ball to Brandao who coolly converted.