Bryan Mbeumo put United ahead shortly after half-time before Tyrique George levelled for the hosts in the 83rd minute at Hill Dickinson Stadium. Benjamin Sesko looked to have won it for the visitors with a header two minutes from time, only for Maitland-Niles to produce a spectacular strike from around 25 yards in the sixth minute of stoppage time to complete the comeback and spark wild celebrations among the home support.
The result arrived at the end of a difficult week for Everton, who saw deadline day end in frustration as a move for Folarin Balogun collapsed, leaving David Moyes with a threadbare squad up front after Iliman Ndiaye and Beto both departed.
Maitland-Niles arrived alongside Jack Grealish as one of the club's late additions, and his introduction from the bench proved decisive on his first appearance for the club.
Speaking to Sky Sports afterwards, Maitland-Niles said the manner of the point felt every bit like a victory.
"It felt like a win. We dug deep and managed to get a point in the end. The crowd were with us and we were fighting to the end and that's why you get those results," he said.
Reflecting on the goal itself, the midfielder described the finish as a moment of instinct.
"It's amazing, everyone wants to start off like that and thankfully I did. The ball fell to me on the edge of the box, I put my foot through it and it ended up in the top corner which I'm happy about," he said.
Maitland-Niles also spoke about the impression he was determined to make in his first outing for the club.
"I came in to work hard. It's a team full of hardworkers so I fit right in. I'm going to show I can fit right in and pull my weight and give as much as everyone else, if not more," he said.
Manchester United, under Michael Carrick, had appeared to be closing in on a first away win since their defeat at Hull City, with Bruno Fernandes striking the crossbar in the eighth minute before Mbeumo and Sesko put the visitors in control either side of George's equaliser.
Marcus Rashford had also caused problems throughout down Everton's right flank, but it was Maitland-Niles' intervention that ultimately settled the contest, denying United what would have been a morale-boosting victory on the road.