Brabham, the youngest son of Australian Formula One legend Jack, shared the 382 laps with Alexander Wurz and Marc Gene, to give the French constructors their first victory in the competition since 1993.
"I am just happy to have won," said Mr Brabham. "I recall my brother Geoff saying he was the only Brabham to have won Le Mans and I am proud to have had the chance to do this. However, it is not a one man show and there are a lot of people at the heart of this team who are responsible for this victory."
Peugeot had been in charge after seven hours of action on Saturday with the French team in three of the top four places.