Kobbie Mainoo's composed finish put the Red Devils ahead midway through the first half, before Newcastle equalised through Anthony Gordon just four minute after the break.
However, Man United regained the lead when Amad Diallo fired his first Premier League goal into the far corner just before the hour mark, before Rasmus Hojlund required only three minutes to make an impact off the substitutes' bench and score the hosts' third.
Lewis Hall provided the Magpies with a glimmer of hope in stoppage time when he curled a sweet strike past Andre Onana from 20 yards, but the Red Devils held on for what could prove to be a pivotal victory in their quest to secure Europa League football for next season.
Erik ten Hag's men remain eighth in the table, but they have moved level on points with Eddie Howe's Newcastle, who have slipped to seventh after Chelsea beat Brighton & Hove Albion to climb up to sixth place, sitting three points clear of both the Magpies and the Red Devils with only one game remaining.
Kobbie's calm finish gives Man Utd narrow lead
Newcastle's travelling supporters were in full voice and their team made a bright start to the contest, putting pressure on Man United's backline within the first few minutes. Sofyan Amrabat made a vital sliding challenge to prevent Gordon from striking at goal inside the area following a promising burst forward from the visitors.
Man United responded well and their first chance of the evening came from a set-piece, with Fernandes's free kick initially punched away by Martin Dubravka, before Amrabat's header back into the mixer was met by an audacious overhead kick from Casemiro which flew just over the crossbar.
Fernandes was pulling the strings as Man United chief creator throughout the match, even though he was operating in a more advanced role than usual, and he was involved in a neat give-and-go with Alejandro Garnacho before the latter's shot was saved by Dubravka, who narrowed the angle well at his near post.
Man United were on top and their persistence in the final third was rewarded just after the half-hour mark when Mainoo collected a pass from Diallo, that took a slight deflection of Fernandes's heel, before taking a touch and nonchalantly placing his shot into the bottom-left corner from around eight yards out - his third Premier League goal of the season.
Newcastle looked to hit back immediately as Longstaff's cross from the right rolled across the six-yard box; it was begging to be tapped home, but Alexander Isak opted to pull away as he anticipated a cut-back.
Casemiro, who has received widespread criticism in recent weeks, then made a crucial last-ditch tackle to stop Gordon in his tracks, before heading the ball off the line to deny a towering Dan Burn at the back post.
Amad, Hojlund inspire Man Utd to crucial three points
Just like the first half, Newcastle buzzed out of the traps and within the space of four minutes, they restored parity after Jacob Murphy curled a delightful cross into the six-yard area for Gordon to slide the ball home - his 11th Premier League goal of the campaign.
The Magpies then looked destined to take the lead just a few minutes later when Gordon broke free from the halfway line and teed up Isak in a central position, but Amrabat came to the rescue and made a remarkable block that looped onto the crossbar.
That missed chance proved costly for Newcastle as they fell behind again just before the hour mark. Fernandes's poor corner was headed away at the near post by Murphy, but he picked out Diallo who arrowed a brilliant left-footed strike into the far corner before celebrating right in front of the Newcastle supporters.
Newcastle continued to pose a threat and Onana was called into action to make two important saves, firstly keeping out Longstaff who had been played through down the left channel, before making a superb acrobatic save to tip Joelinton's towering header over the crossbar.
Joelinton, Fabian Schar and Miguel Almiron were all brought on by Howe for the final half-hour and the latter came agonisingly close to netting a Magpies equaliser, but he was unable to meet Gordon's fizzed delivery across the face of goal.
Diallo received a standing ovation as he left the field 10 minutes from time, and his replacement Hojlund needed just three minutes to get his name on the scoresheet and put the game to bed; charging past Burn before slotting a right-footed shot into the bottom corner.
Newcastle gave themselves hope of pulling off a late comeback when left-back Hall pounced on a headed clearance form Casemiro before firing a brilliant left-footed shot into the far corner.
However, Man United held on for three valuable points in their final home game of the season; they will travel to Brighton for their last remaining fixtures on Sunday, the same day Newcastle make the trip to Brentford.