The Senegal midfielder was shown his marching orders by referee Tony Harrington in the 13th minute after putting his hand to Keane’s face following an angry altercation.
The home crowd anticipated waves of attack but United failed to take advantage of their numerical advantage, proving toothless against David Moyes’ battling team.
Instead it was 10-man Everton who found the net, taking the lead courtesy of a wonderful strike by Kiernan Dewsbury-Hall in the 29th minute.
Dewsbury-Hall received the ball and surged towards goal, beating Bruno Fernandes and Leny Yoro before bending the ball into the top corner.
United huffed and puffed for the rest of the half, with Everton goalkeeper Jordan Pickford clawing away a Fernandes shot from distance as the half-time approached.
Ruben Amorim, marking the first anniversary of his maiden game in charge of United, brought on Mason Mount for Noussair Mazraoui at half-time but his team created little despite dominating possession.
Amorim threw on midfielder Kobbie Mainoo and Diogo Dalot for Casemiro and Yoro in the 58th minute but still United looked blunt.
Pickford kept out a powerful Joshua Zirkzee header with just over 10 minutes of normal time to go and Everton hung on for a famous win.
United came into the match at Old Trafford on the back of a five-game unbeaten run.
Everton suffered a big blow in just the 10th minute when they lost captain Seamus Coleman.
But worse was to follow three minutes later with the scarcely believable bust-up between Gueye and Keane.
Gueye is the first Premier League player to be sent off for fighting with a teammate since 2008.
The Premier League Match Centre posted on X: “The referee’s call of red card to Gueye for violent conduct was checked and confirmed by VAR – with the action deemed to be a clear strike to the face of Keane.” (AFP)
