The home side started strongly in the early stages of the game, winning dangerous free kicks and corners to put Bordeaux under pressure.
Henri Saivet had the away side's first real chance of the game, but he could only shoot over the bar after a flowing team move.
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Sertic had another effort just before half time and almost surprised David Ospina, who could only punch away the shot from distance.
Ospina had to be stretchered out on 51 minutes and was replaced by 16-year-old reserve goalkeeper Anthony Mandrea.
Saivet tried to test the young keeper, but he could only put his header wide from a fine cross.
Ludovic Obraniak made it 2-0 on 59 minutes, smashing his shot straight past the goalkeeper to double his side's lead.
The referee awarded Nice a penalty on 76 minutes, which was put away by Dario Cvitanich to make it 2-1.