Doucoure played a starring role, setting up Andros Townsend's equaliser with a gorgeous turn and pass which took out the entire opposition defence.
The French midfielder has had an incredible start to the season under new Toffees manager Rafael Benitez, racking up two goals and four assists in the league, already beating his tally from the last campaign.
Doucoure has taken up a more attacking role under the Spaniard, and has started the season so well that talkSPORT host Tony Cascarino believes he's the best midfielder in the division.
"I can't think of a better midfielder at the moment than Doucoure in the Premier League, the way he's playing in this advanced role," Cascarino said on the Weekend Sports Breakfast.
"He is playing brilliantly, he's really playing well."
Manchester United supporters clambered for a midfield signing this summer, despite bringing in Cristiano Ronaldo, Jadon Sancho and Raphael Varane.
Cascarino believes Doucoure showed United exactly what they need, bossing the likes of Fred and Scott McTominay during the draw.
"Look at United's midfield and you think, that's what they're screaming out for, a Doucoure type of midfielder," he said.
The 28-year-old was signed from Watford in 2020, and is now hitting the heights many thought he could after leaving Rennes in Ligue 1.
Doucoure has attributed his massive improvements this season to new manager Benitez, who has helped increase his understanding of the game
"I am very happy with the games I've played this season and I am learning with the manager every day," Doucoure said. "Everything changed in my game and my understanding of the game improved.
"The manager gave me a lot of advice, simple advice that makes a difference, and I try to take that on the pitch and help the team as much as I can."
Meanwhile, Benitez has commented on Doucoure's attacking output, saying he's encouraged the Frenchman to attack the opposition penalty area.
"With Doucoure, it's clear he has the energy and potential to get in the box, I told him so many times 'Go'," Benitez said.
"He's doing well and focused on that, so I'm really pleased. That is an extra motivation for any player."