The Hammers were always facing an uphill struggle following the controversial dismissal of Feghouli after just 14 minutes.
The Algeria international was making his first Premier League start of the season but he was desperately unlucky to receive a red card following a challenge with United defender Phil Jones.
The decision changed the course of the game and United made the extra man count as second half goals from Mata and Ibrahimovic handed them all three points.
Despite being down to ten-men for the majority of the game, Slaven Bilic can still be pleased with the battling display his players produced and will be hoping they can get straight back on the winning trail when they host Manchester City in the Emirates FA Cup third round at London Stadium on Friday night.
It could have been a different story if the Hammers had broken the deadlock after just ten minutes following a great move which resulted in a neat interchange between Manuel Lanzini and Dimitri Payet and the Argentine midfielder saw his low shot superbly turned round the post by David de Gea diving low down to his left.
But the major talking point of the game arrived on 14 minutes following the harsh dismissal of Feghouli.
Referee Mike Dean shocked the home crowd when he pulled out a red card and reduced the Hammers to ten-men after he adjudged the Algeria international had committed a professional foul on Jones.
The decision infuriated Bilic and his backroom staff and the Hammers manager was forced to change his system and revert Michail Antonio from a central striking role into a wide position.
United were keen to make the extra man count and thought they had broken the deadlock on 35 minutes after Henrikh Mkhitaryan played the ball across to Antonio Valencia who had the goal at his mercy but he saw his close-range shot produce a superb save from Darren Randolph.
The rebound fell to Jesse Lingaard who had an open goal to hit the ball into but he struck his effort against the post.
United could have been made to pay as the Hammers created their best chance of the first half on the stroke of half-time.
Antonio ball into Lanzini who curled a right-foot shot from the edge of the box which produced another fine save from De Gea.
The Hammers showed all their fighting qualities and came close again on 53 minutes when Payet's free-kick fell perfectly for Antonio who rose above the United defence but he directed his header wide of the post.
Bilic must have sensed it was not going to be West Ham's day after Antonio had another golden chance to open the scoring on 59 minutes but failed to convert his chance.
Lanzini played the perfect through ball into the path of the Hammers forward who was through on goal but he saw his shot kept out by the legs of De Gea.
United made the home side pay as they finally broke the deadlock on 62 minutes.
Substitute Marcus Rashford cut the ball back for Mata and he fired the ball past Randolph into the corner of the net.
Ibrahimovic sealed the victory for United on 77 minutes after Pedro Obiang's clearance hit Ander Herrera and the ball fell to the experienced forward who struck a low powerful shot into the corner of the net.
West Ham: Randolph, Nordtveit, Reid, Ogbonna, Cresswell; Kouyate (Fernandes 82), Obiang; Feghouli, Lanzini (Ayew 88), Payet (Carroll 69); Antonio
Subs not used: Adrian, Noble, Fletcher, Quina
Bookings: Payet, Nordtveit
Red Card: Feghouli
Manchester United: De Gea, Valencia, Jones, Rojo, Darmian (Mata 46), Ander Herrera, Carrick, Pogba, Mkhitaryan (Smalling 62), Ibrahimovic, Lingard (Rashford 58)
Subs not used: Martial, Young, Romero, Fellaini.
Bookings: Darmian, Valencia
Referee: Mike Dean (Wirral)
Attendance: 56,996