Norgaard was given his marching orders in the 41st minute after he caught Jordan Pickford with an outstretched right leg.
The Denmark international attempted to reach Ethan Pinnock's header towards the far post, but he was unable to reach the ball and instead collided with the Everton goalkeeper.
Referee Chris Kavanagh was sent to the monitor following consultation with VAR, before he decided to show Norgaard a straight red card for dangerous play.
Despite being left a man light, Brentford managed to frustrate Everton to clinch a useful point from their trip to Goodison Park.
Brentford win Norgaard appeal
Brentford head coach Thomas Frank was left angered by Norgaard's sending off, insisting that the officials should have stuck with the on-field decision.
"For me it is not a red card," Frank told reporters after the goalless draw. "I see a situation where it is coming across the six-yard box, Christian's eyes are clearly on the ball and he is stretching to try to touch it behind [Yoane] Wissa, Wissa is going at the the ball, just changing the direction of the ball.
"Chris was unlucky his studs go on the leg of Pickford. No intention, he is actually pulling out of full force with no intention of making a foul, just trying to score.
"Where is that that bit of common sense? I don't know exactly the law of the game but if that is a red card then the game has changed. The ref has been told to take on-field decisions, which in my opinion was a good on-field decision but was overturned by VAR. If it is not the law or the rule then Chris [Kavanagh] was not brave enough to overturn the situation."
Frank will be pleased to hear that Brentford has successfully won their appeal to overturn Norgaard's red card.
An FA statement read: "Christian Norgaard will be available for Brentford's next three matches following a successful claim of wrongful dismissal"
"The midfielder was sent off for serious foul play during the Premier League match against Everton on Saturday, 23 November."
Norgaard to be available for Leicester fixture
Norgaard was set to serve a three-match suspension, but the FA's decision means he will be available for Brentford's upcoming fixtures against Leicester, Aston Villa and Newcastle United.
Having started all 10 of his Premier League appearances this season, Norgaard should be in the lineup for Saturday's fixture at the Gtech Community Stadium.
The Bees will face a Leicester side that are currently searching for a new manager following the recent sacking of Steve Cooper.
Brentford will be hoping to continue their impressive record at the Gtech Community Stadium after winning five and drawing one of their six Premier League home matches this season.