Maitland-Niles’s arrival from Lyon on the final day of the transfer window was overshadowed by Everton’s failure to reinforce their attack.
But the former Arsenal full-back lasered a long-range shot into the top corner in the 96th minute to punish a lacklustre United performance.
Bryan Mbeumo fired United in front inside the first minute of the second period.
But an Everton side short on attacking options rallied to level through Tyrique George.
Substitute Benjamin Sesko’s header looked to have won United all three points.
But the decision not to reinforce Michael Carrick’s defence will face more scrutiny as United have conceded twice in all of their opening three games of the Premier League season.
“It feels like a defeat,” said Carrick. “We’re bitterly disappointed to be up in the position we were in the game twice, so close to the end… it’s not a great feeling.”
A draw maintains Everton’s unbeaten start and keeps them one point ahead of United to calm the sense of unrest among the club’s fans.
“It was a brilliant goal and I thought it was a big moment for the crowd as well, I think it was good for them,” said Everton boss David Moyes.
A miserable end to the window could still have ramifications for Everton’s performance over the rest of the season.
After letting Iliman Ndiaye depart in a £65 million (US$88 million) move to Manchester City and Beto to leave for Fiorentina, the Toffees expected to strengthen their forward line with the signing of Monaco’s Folarin Balogun.
An issue with the USA international’s medical saw the clubs frantically renegotiate the structure of a £40 million deal but Balogun turned his back on the move.
Moyes has been left with only one natural striker to pick from in Thierno Barry as a result and only 18 outfield players.
The return of Jack Grealish on loan for the season only slightly softened the blow as Moyes faces up to the realities of a possible relegation battle rather than a challenge for European football.
Bruno Fernandes scored a hat-trick as United thrashed Ipswich 5-2 last weekend to get their season up and running after a dreadful 2-0 defeat at Hull.
The United captain came closest to breaking the deadlock in a first half otherwise devoid of quality when his volley came back off the crossbar.
A sleepy start to the second by Moyes’s men proved costly as Mbeumo was allowed to bear down on goal on his favoured left foot and arrow a shot beyond Jordan Pickford.
United, though, failed to build on their advantage and the introduction of Grealish off the bench lifted the home crowd.
Kiernan Dewsbury-Hall twice failed to connect sweetly with clear sights of goal.
But the visitors’ luck ran out seven minutes from time when Hayden Hackney fed George and the former Chelsea winger blasted into the top corner from a narrow angle.
Sesko’s involvement has been limited at the start of the campaign due to an injury in pre-season, but the Slovenian looked sharp as he stooped to head in Luke Shaw’s cross to restore United’s lead.
The Red Devils never looked comfortable at the back but could not have foreseen the manner of the equaliser.
United looked to have cleared the danger with the five minutes of added time up, but the ball broke to Maitland-Niles who swept a curling shot into the top corner. (AFP)