Matt Ritchie scored the only goal in the second half as the Magpies climbed out of the relegation zone and left the visitors 16 points adrift of leaders Manchester City.
The Red Devils missed a string of chances to take something from a ground at which manager Jose Mourinho is yet to win a league match.
But debutant Martin Dubravka was excellent in the Newcastle goal, denying Jesse Lingard, Anthony Martial, Ashley Young and Michael Carrick.
And the hosts could have had a first-half penalty when Chris Smalling tripped Dwight Gayle.
Defeat for Manchester United raises the prospect of Manchester City being crowned champions when the teams meet at Etihad Stadium on 7 April.
Should both teams win all of their league matches prior to that, City would only need to draw with their fierce rivals to secure the title that day.
Mourinho said after the game that Newcastle had fought "like animals" - and the hosts certainly produced a fierce and committed performance.
The Magpies made more sprints (553 to their opponents' 490), ran further (115km to 105km), and in DeAndre Yedlin and Ritchie had the game's fastest and most industrious players.
Manager Rafael Benitez may be hoping recent signing Islam Slimani, who missed this game, can add more to an attack that only managed three shots on target, but Ritchie was clinical when it mattered.
Smalling was penalised for a dive that allowed the impressive Jonjo Shelvey to send in a free-kick. The equally eye-catching Florian Lejeune headed it down, and Ritchie collected Gayle's flick to shoot past David de Gea.
That ended a run of 43 shots without a Premier League goal for Ritchie - and gave Newcastle their first home win in the league since 21 October.
Prior to the match they were just one point better off than in their 2015-16 relegation season, but this win moved them up to 13th - and only three points behind 10th-placed Bournemouth.
Same team, similar problems to Wembley
Mourinho's decision to select the same starting XI that lost convincingly to top-four rivals Tottenham last month may have unsettled some visiting fans.
But, while the Red Devils were much better here than during an abject display at Wembley, some familiar flaws resurfaced.
Then, Phil Jones missed a crucial first header in the build-up to Christian Eriksen's early goal. Here, nobody tracked Lejeune as he ran between Nemanja Matic and Paul Pogba to head down for Ritchie to score.
Smalling won just 53% of his headed duels, compared to 77% and 75% respectively for Newcastle's central-defensive pairing of Lejeune and Jamaal Lascelles.
It suggests a defensive diffidence at odds with a manager who traditionally builds title-winning teams from the back.
Overall, the visitors had the better chances but were thwarted by Dubravka, who notably stuck out a leg to deny Martial as he latched onto a wonderful, defence-splitting pass from Nemanja Matic in the first half.
Had that chance - or a header from the French forward - gone in, there may well have been a different outcome.
Instead, with Spurs and Liverpool increasing the pressure on them, Mourinho's side must assert more aerial dominance and show better focus at the back.
Man of the match - Martin Dubravka (Newcastle)
Geordie jinx goes on for Jose - the stats
- Mourinho has never won a Premier League match at St James' Park (P7 W0 D3 L4) and has managed more away league games at Newcastle without winning than at any other club in his career.
- Mourinho has lost six times against Benitez in all competitions. Only against Pep Guardiola (nine) has he suffered more defeats as a manager.
- Newcastle enjoyed their first win in nine Premier League home games (D3 L5), since beating Crystal Palace in October.
- Manchester United have lost five games in the Premier League this season, equalling their tally for the whole of last season.
- Ritchie ended a run of 43 shots this season without scoring in the Premier League, which was the longest such run in the division.
- Gayle has had a hand in a goal in both of Newcastle's Premier League matches against Manchester United this season, scoring at Old Trafford in November before assisting Ritchie here.
- The Red Devils have won only one of the nine Premier League matches this season after conceding the opening goal of the game (D3 L5) - a 4-1 win over Newcastle in November.
- Manchester United have had three players booked for dives in the Premier League this season (Valencia, Herrera, Smalling), a joint high along with Bournemouth.
'We could have been here 10 hours and not scored' - what they said
Manchester United manager Jose Mourinho on Match of the Day: "My verdict is we could've been here for 10 hours and not scored a goal. Newcastle played with their lives and defended with their lives.
"They got from us a defensive mistake and from a lateral free-kick they scored. The gods of football were clearly in their side. They must have an amazing feeling after giving absolutely everything
"We had some [chances] with the score at 0-0. Alexis [Sanchez] had an open goal and then the countless opportunities of the last 20-25 minutes. The double [miss] of Martial is incredible in the last minute."
Newcastle manager Rafael Benitez said: "We worked as hard as other games, but against a team like Manchester United every ball is important, they can punish you, so you work like them. Amazing effort.
"They are dangerous, but the teamwork we showed to fight for every ball was amazing. I am pleased for the players and the fans. Because we won here at home.
"We had games in past when conceded late. We got lucky with some shots, but we showed the character, the commitment and the desire today."
On Martin Dubravka's debut: "He can buy the lottery and win today. He was composed and that gave confidence to the team. All the players worked hard, so it is not fair to say just the goalkeeper played well."
Manchester United travel to Huddersfield in the FA Cup fifth round on Saturday, 17 February (17:30 GMT), while Newcastle head to Bournemouth in the league on Saturday, 24 February (15:00 GMT).