Sunderland dominated possession in the first half at the Hill Dickinson Stadium but didn't have a single shot on target and trailed at the interval after Merlin Rohl's deflected opener just before the break.
But Sunderland came roaring back after the break - with the help of some match-winning substitutions - and goals from Brian Brobbey, Enzo Le Fee and Wilson Isidor secured a victory that lifted the Black Cats to ninth, just a point behind Brentford in eighth and two shy of seventh placed Brighton.
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Le Bris said: "I'm happy. Against a tough opponent in a tough place, the result went well.
"It wasn't easy. The first half we had control without the ability to threaten the opponent box really.
"We considered a goal from set-pieces second phase. It's a bit unlucky but we knew they were strong at this phase.
"During half-time we agreed it was important to take more risks, even if the game became a bit more unbalanced with transitions. It went well."
Le Bris' substitutions also made a huge impact, with Isidor and Chris Rigg combining to tee up Le Fee for Sunderland's second goal and Habib Diarra, also introduced from the bench, assisting Isidor for the third in stoppage time.
Le Bris said: "It's really important to mention that. Our subs gave extra energy, more pressing and a bit more composure as well with the end product."
Le Bris was forced into his first change after just 20 minutes when Omar Alderete went off injured. Luke O'Nien took his place and enjoyed what was probably his best performance of the season so far.
"Omar got a small injury during the week," Le Bris explained.
"He was confident he could manage the game but in a sprint he felt it a little bit so we decided to avoid something major and we'll see how he is tomorrow.
"Luke was excellent, as expected, which is really important. I repeat our subs are really important because you can't manage a game with only 11 players. Luke was good here in the FA Cup and good again today."