Manchester United looked to be heading for all three points at Goodison Park but a late penalty saved Everton.
The game finished 1-1 with Leighton Baines converting from the spot after Zlatan Ibrahimovic had given United the lead.
It was a game largely dominated by United but they failed to convert the chances to make the game safe and were left to settle for a point with the top four looking a distant prospect.
Both teams made changes for the game, Ronald Koeman, after suffering defeat at his old club Southampton, dropped captain Phil Jagielka with Ramiro Funes Mori replacing him.
Man United had Wayne Rooney unavailable through suspension, with Anthony Martial and Henrikh Mkhitaryan coming into the starting line-up.
United took the lead just before the break, Martial putting a high ball into the box which the Everton keeper Maarten Stekelenburg came out for, but didn't reach and Ibrahimovic lobbed him, the ball just crossing the line after coming off the bar.
The visiting side looked in control and seemed more likely to score another to settle the game. They went close, especially when Ander Herrera hit the woodwork.
However, the longer the game went on Everton had chances of their own and they made United pay on 88 minutes when United sub Marouane Fellaini fouled Idrissa Gueye in the area and Baines gave David de Gea no chance from the spot.
That late equaliser gave the hosts momentum and they could have snatched all three points late on but that would have been harsh on Jose Mourinho's team.
United are now sixth in the Premier League but nine points off fourth placed Manchester City. Everton stay in eighth position.
United are in action in midweek, playing Zorya Luhansk \away in the Europa League.
United are 2/5 to win the Europa League.
Their next league match is at home to Tottenham next Sunday.
They are 23/20 to win the game, Spurs are 1/1 with the draw priced at 1/1.
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