Wilson Isidor and Habib Diarra came off the bench to combine for the decisive moment, with the Haiti international sealing the win at the Stadium of Light.
The goal capped a memorable week for Isidor, who celebrated his birthday and signed a new contract with the club.
Le Bris was delighted with the contribution of his substitutes and the support from the home crowd.
“Fulham are a good team and very good on the ball,” Le Bris told club website.
“We defended well - that was the first pillar of this game. We had to manage their rotations and the way they move in behind.
“We were impressive in the first half - we were good on the ball but didn’t create many chances. It was tight and tactical.
“Our substitutes helped a lot, and it is so good to feel the energy of the squad.
“It is obvious for Sunderland and for everyone in this league - you can’t play with just eleven in this league.
“The Premier League is really demanding, but we really enjoyed being back at home.”