The result against the Blues capped a remarkable season in which the Black Cats finished seventh in the Premier League during their first campaign back in the top flight, sealing European football for the first time in over 50 years.
Trai Hume opened the scoring with a superb volley on 24 minutes before Malo Gusto turned the ball into his own net shortly after half-time to double the hosts' advantage.
Chelsea responded through Cole Palmer, but their hopes were dented when Wesley Fofana was sent off for a second yellow card.
“It feels incredible and it shows that we kept our high standards until the end. The last three or four games showed that we are still ambitious - it was fantastic," Le Bris told the media.
“We were well prepared for today. The sessions this week were good, so we were ready to play.
“We knew we were facing a strong opponent, so we had to look after the ball well, create big chances and score goals.
“It was a bit tense, but the players did well with great consistency and discipline - it was good.
“It is crazy. The 24th of May is the perfect day when you think about last season with our late promotion, and now we are into the Europa League.
“It shows the consistency of the Club, the togetherness, the alignment - when you have this, you can achieve something exceptional.
“We have to reset quickly and prepare for next season. The Premier League will be our first focus, obviously."