A late Leighton Baines penalty cruelly denied United a sixth league win of the season as Everton fought back for a point.
Zlatan Ibrahimovic put United ahead with a clever lob but Marouane Fellaini, who had just come on, then clumsily tangled with Idriss Gueye and Baines stroked in the spot-kick.
Marcos Rojo was fortunate not to be sent off and Ander Herrera struck the bar as United once again failed to see out a match they should have won.
In contrast to our excellent cup form, we've only won one in ten league games and this was a third successive draw that sees us stay sixth.
Eric Bailly was named in a matchday squad for the first time since October but it was his replacement in the team that survived a let off inside the opening ten minutes.
Marcos Rojo's late, lunging challenge on Gueye should have seen him sent off, but referee Michael Oliver only saw the tackle as a yellow card offence.
Gareth Barry was then equally as fortunate not to receive his marching orders following a late tackle on Ibrahimovic moments later.
Yannick Bolasie lashed an effort wide after Romelu Lukaku had played him in, while Ibra went close with a 20 yarder at the other end.
United moved ahead through their first shot on target three minutes shy of the interval.
Maarten Stekelenburg had a rush of blood to the head and came racing out, which allowed Zlatan to lob the advancing keeper and his effort struck the bar, bounced off a post and trickled over the line.
Ramiro Funes Mori thought he had cleared the ball but goal-line technology proved otherwise and United took a lead into the interval.
Everton had been poor in the first half and started the second brightly, perhaps fuelled by the half-time words of their under pressure boss Ronald Koeman.
David de Gea saved well from Kevin Mirallas and Anthony Martial went close with a deflected effort.
United had a penalty appeal waved away after a Baines handball and Herrera, who impressed again, almost doubled the lead when he rattled the bar on the hour mark.
Everton upped the ante as De Gea found himself increasingly busy: he beat away Gueye's rasping 25-yard drive, and then tipped over a close-range header from substitute Mason Holgate.
Another replacement, Enner Valencia, was also denied by the United stopper as the visitors sat deep and looked to hold on to their slender advantage.
Fellaini was introduced to try and see the game out but instead cost his side the game when he fouled Gueye inside the area.
Baines made no mistake from the spot and, despite five added minutes, both sides had to settle for a point.
Overall team performance: 6/10
United Faithful Man of the Match: Phil Jones