Man United looked set to win by Jose Mourinho's favourite 1-0 scoreline, but a clumsy Marouane Fellaini challenge gifted Everton a life-saving penalty in the dying minutes.
The ginger-afroed midfielder had only been on the pitch a matter of minutes before he gifted Leighton Baines the spot kick.
The Red Devils had led for most of the game through Ibrahimovic's taekwondo-kick which lobbed blundering Toffee's keeper Stekelenburg who had rushed off his line.
It was the Swede's sixth goal in his past five games.
Early on, Marcos Rojo should have seen red for a horror tackle, jumping off the ground and going in with both feet, but managed to somehow escape with just a caution.
Man-of-the-match Idrissa Gueye was fortunate to come out of the challenge with both legs.
Fans couldn't believe it.
Mourinho said after the game: "We were the best team by far... but we didn't win. We don't get the results we deserve.
"In every one of our draws, we were much closer than the opponent to win."
Asked about Fellaini and Rojo, the taciturn Portoguese replied: "No comment"