The North-East outfit launched an appeal to the Football Association after referee Kevin Friend dismissed Brown, despite appearing to fairly win the ball, during the Black Cats' 2-0 defeat to Stoke City on Saturday.
Head coach Gus Poyet told the club's official website: "I would like to express my thanks to the panel for giving the matter their consideration. Naturally we are delighted with their decision, which is fair and just.
"I have spoken with Mike Riley (manager of the PGMOL) and while the details of our conversation will remain private, I am satisfied with today's outcome.
"Of course it was hugely frustrating to have Wes sent off, but we accept that officials are only human and like everyone, they can make mistakes."
Brown will now be available for Sunderland's Premier League match against Aston Villa on Saturday.