The full-back drilled home a superb 90th-minute equaliser to end a run of four successive defeats in all competitions after Wayne Rooney looked to have claimed the points for the visitors.
Rooney had opened the scoring with a ninth-minute penalty and Jesse Lingard made it 2-0 eight minutes before the break.
But Georginio Wijnaldum and Aleksandar Mitrovic gave the home side hope and although Rooney scored again 11 minutes from time, Dummett's late intervention denied Louis van Gaal victory on a night when he may well have been angry, but could not have been bored.
A crowd of 49,673 at St James' - among them new signings Jonjo Shelvey and Henri Saivet - rose before kick-off to pay its respects to the late Pavel Srnicek, the man between the posts on the day almost two decades ago that Newcastle famously beat Sir Alex Ferguson's side 5-0 on Tyneside.
But once the game was under way, referee Mike Dean did not endear himself to the locals when he awarded the visitors a penalty for handball against Chancel Mbemba as he contested a corner with Marouane Fellaini, although how much the defender knew about it was debatable.
Rooney, however, needed no second invitation as he dispatched the spot-kick with Mr Dean, who later decided not to repeat the dose at the other end after Daryl Janmaat went down in the box under Lingard's rash challenge, having been firmly installed as the villain of the piece.
Van Gaal's men extended their lead seven minutes before the break when, after Mbemba's loose pass had been picked off, they broke at pace and Rooney held the ball up before feeding a fine reverse pass to Lingard to score.
But Newcastle grabbed a lifeline four minutes later when Mitrovic headed down Fabricio Coloccini's long ball and Wijnaldum swept it past David de Gea for his club's first goal since December 19.
The Magpies returned in determined mood and went close seven minutes after the restart when Moussa Sissoko tricked his way past full-back Ashley Young and forced De Gea, who had produced a vital first-half block to deny Wijnaldum, to save again at his near post.
Lingard could have effectively sealed victory four minutes later, but shot high and wide with the goal at his mercy after being set up by Ander Herrera, but after Jack Colback had seen fresh appeals for a penalty waved away, Mr Dean finally pointed to the spot after Chris Smalling had hauled down Mitrovic.
The Serbia international dusted himself down to convert calmly from 12 yards to level, and the Magpies thought they had taken the lead two minutes later when Wijnaldum struck, but did so from an offside position.
Rooney looked to have won it with a stunning 79th-minute finish after substitute Memphis Depay's initial shot had been blocked, but Dummett grabbed a point at the death with a left-foot missile.
TWEET OF THE MATCH
"This is what @premierleague is all about
Energy, goals and the passion of the players + fans!! #mufc" - former Manchester United goalkeeper Edwin van der Sar was amongst those taken in by Tuesday's encounter
Rob Elliot: 7
Daryl Janmaat: 7
Chancel Mbemba: 6
Fabricio Coloccini: 7
Paul Dummett: 6
Cheick Tiote: 6
Jack Colback: 6
Moussa Sissoko: 7
Ayoze Perez: 7
Georginio Wijnaldum: 8
Aleksandar Mitrovic: 7
Yoan Gouffran: 6
Ivan Toney: 6
Siem de Jong: 6
David de Gea: 7
Ashley Young: 6
Chris Smalling: 6
Daley Blind: 6
Matteo Darmian: 7
Morgan Schneiderlin: 7
Marouane Fellaini: 6
Anthony Martial: 7
Ander Herrera: 7
Jesse Lingard: 7
Wayne Rooney: 8
Memphis Depay: 7
Juan Mata: 6
Wayne Rooney was involved throughout, calmly converting his penalty, setting up Jesse Lingard for his goal and then smashing home the third.
MOMENT OF THE MATCH
Paul Dummett's piledriver which secured a precious point from a game in which he and his team-mates fought desperately hard to gain tangible reward.
VIEW FROM THE BENCH
Steve McClaren will have been delighted with the way his side fought to the death on a night when several key decisions went against them, but finally found their touch in front of goal
Louis van Gaal will have been happy with the way United attacked, if not with all of their finishing, but they were suspect at the back.
MOAN OF THE MATCH
Referee Mike Dean needed eyes in the back of his head on a night when there were penalty decisions to make at both ends
All were tight calls and the two he gave were probably correct, but he looked to have missed a third.
WHO'S UP NEXT
Newcastle v West Ham (Barclays Premier League, Saturday, January 16)
Liverpool v Manchester United (Barclays Premier League, Sunday, January 17)
It was a thoroughly entertaining match but one which left Manchester United boss Louis van Gaal frustrated.
"Of course it feels like a defeat," the Dutchman told broadcast media.
"We have given it away - I have told that to my players
When the referee gives a penalty for nothing - it is a duel I think and you cannot decide who is worse - but we gave it away.
"We could have scored six goals easily here and we did not
If we had, it would have been three successive wins at the start of the year going into Liverpool.
"It is not so interesting to create chances
In every press conference I say you have to score one more goal than the opponent."
United captain Wayne Rooney echoed those sentiments, but Newcastle boss Steve McClaren believes his side deserved a point.
"The crowd responded magnificently and we wanted to show everyone what we are about," he said.
"People said that United were boring and that we lack character, but we kept fighting until the end and we have got a goal that feels like a winner.
"People thought it would be a 0-0 and it was a classic at 3-3
It must have been a great game for the neutral - it was a heart attack for the coaches."
Source : PA