Rasmus Hojlund marked his 21st birthday with a superb opener midway through the first half, before Alejandro Garnacho netted twice in the second half to help the Red Devils claim their biggest home win of the season.
West Ham had their fair share of chances, particularly in the first half, but they ultimately lacked a cutting edge in the final third and have subsequently seen their six-game unbeaten run in the top flight come to an end.
Erik ten Hag's men slipped to eighth place before kickoff following Brighton & Hove Albion's win over Crystal Palace on Saturday, but victory over West Ham has has seen them climb above the Hammers into sixth spot, albeit still eight points adrift of the top four.
David Moyes's side, meanwhile, have slipped down to seventh spot as a result of their defeat at Old Trafford and sit two points behind the Red Devils.
The headline team news from Man United's perspective prior to kickoff was the return of Harry Maguire in central defence, with the Englishman - starting his first game since mid-December - replacing Raphael Varane to partner Lisandro Martinez, who passed a late fitness test to retain his starting spot.
As for West Ham, Moyes opted to make two changes to the side that drew 1-1 with Bournemouth on Thursday, with Manchester City loanee Kalvin Phillips and Konstantinos Mavropanos replaced by Vladimir Coufal, who returned from suspension, and Nayef Aguerd, who made his comeback after representing Morocco at the Africa Cup of Nations.
Following a well-observed moment of applause to commemorate the 66-year anniversary of the Munich Air Disaster, both sides made a relatively scrappy start to proceedings as they adjusted to the blustery conditions at Old Trafford, with West Ham pressing well as Man United dictated play from midfield.
The first chance of the contest fell to West Ham with the game's first corner in the 11th minute when Tomas Soucek flicked on a header that deflected goal-bound off Edson Alvarez, forcing Andre Onana to make an instinctive one-handed save to his left inside the six-yard box.
Bruno Fernandes then tested Alphonse Areola from range with a dipping shot before a effort from Soucek deflected narrowly wide for a corner, but the Red Devils soon went up the other end to break the deadlock courtesy of a superb strike from Hojlund on the 23-minute mark.
Casemiro did brilliantly to regain possession inside West Ham's half and his unorthodox interception was collected by Hojlund, who swivelled and shifted the ball onto his weaker right foot before rifling a powerful shot from the edge of the area into the bottom-left corner.
There was no change to West Ham's offensive approach following Man United's opener and they continued to drive forward with intent when in possession; Ben Johnson's strike from distance was palmed to safety by Onana shortly before a tame header from Mohammed Kudus - a livewire down the left flank - was comfortably collected by the Red Devils' shot-stopper.
West Ham ended the first half the stronger of the two teams but failed to register any decent attempts on goal, before Hojlund concluded the half by firing a strike from a tight angle narrowly wide of the near post.
There was a change in goal for West Ham for the second half as Lukasz Fabianski replaced Areola, who was seemingly unable to recover from a knock sustained during a collision with Zouma midway through the first half.
Just three minutes after the break, Man United were given a huge let-off as Maguire was clumsily caught in possession by Emerson, but the Hammers left-back lacked composure when it mattered and scuffed his effort high over the crossbar after bursting through down the left channel.
That missed chance proved costly as the Red Devils went straight up the other end to double their advantage thanks to Garnacho, whose deflected strike from the right side of the penalty area flew past a flat-footed Fabianski at his near post.
The momentum was certainly with Man United and they immediately pushed for a third, with Marcus Rashford drifting inside from the left and firing his shot wide of the far post, before Diogo Dalot curled a 25-yard effort just over the crossbar.
West Ham struggled to carve out any clear-cut chances in the second period, until a ball over the top of United's backline was pounced upon by Jarrod Bowen, but Dalot made an excellent recovery run to slide and block the shot from the Hammers attacker.
Either side of that West Ham chance, Martinez went down in agony on two occasions in the space of five minutes holding his knee; Ten Hag decided to take no chances with the Argentine's fitness and brought on Varane in his place.
Moyes made two changes of his own with Phillips and Maxwel Cornet taking the places of Soucek and Coufal; Phillips had a pop at goal just a few minutes after entering the field but blazed his effort from range well over, shortly after Cornet shanked a shot into a crowded penalty box towards Kurt Zouma, who could only direct his scuffed effort a few yards wide.
West ham continued to push forward in their attempts to pull one back, but Man United put the game to bed six minutes from time when Garnacho slotting a right-footed shot into the far corner after receiving a sweet through-ball from substitute Scott McTominay.
McTominay came close to adding a fourth when he fizzed a low-driven shot narrowly wide from the edge of the box in stoppage time, but United eventually settled for a well-deserved three-goal victory to boost their hopes of securing European football.
Man United will endeavour to claim their third Premier League victory in a row when they travel to the West Midlands to face top-four hopefuls Aston Villa next Sunday, while West Ham test their mettle against title challengers Arsenal at the London Stadium.