The home side were reduced to 10 men later in the first half when Nangis produced a horror tackle on Bordeaux's Wahbi Khazri which resulted in a straight red card.
Khazri tried to make use of the man advantage after the break as he found space to rifle a shot at goal, only to see Caen stopper Remy Vercoutre produce a full-stretch save at his top-right corner.
Not much could separate the two teams in the second half, but Bordeaux took the lead in the 68th minute thanks to Diego Rolan, who finished confidently from Nicolas Maurice-Belay's cross.
Their lead was not to last longer than a few minutes, though, given that Caen's Sloan Privet dragged his side back on level terms with a header to cap off some fine work from Thomas Lemar.
It appeared as though the game was heading for a draw until Dennis Appiah handled in his own area, allowing Rolan to step up and push his side to a slender win with a finish into the bottom-left corner.