Bordeaux fly-half Sanchez scored an early try before Robert Lilomaieva and Jefferson Poirot crossed in the final 12 minutes.
But it was three yellow cards for Dragons forwards that proved just as decisive as the visitors' discipline deserted them at Stade Andre Moga.
Toby Faletau crossed before half-time to hand the Dragons a chance of victory but fellow forwards Andrew Coombs, Lewis Evans and Robertt Sidoli were all binned to leave the visitors facing an uphill struggle.
Dragons, who beat Bordeaux 40-22 last week, remain three points behind Bath who face Rugby Mogliano on Saturday and in the driving seat for a place in the last eight.
- Sports & Recreation
- Jefferson Poirot
- Andrew Coombs