The home side back to their winning ways after Rooney swept in a Rafael cross and Robin van Persie rifled in a low shot.
Diafra Sakho pulled one back with a good header before Rooney got sent off for a reckless tackle on Stewart Downing.
Enner Valencia shot wide and Kevin Nolan had a goal disallowed for offside as the home side held on.
There was obvious relief at Old Trafford when the final whistle was blown, while there was also anger at referee Lee Mason for his decision to dismiss Rooney.
The England striker kicked out at Downing as West Ham threatened to launch a counter-attack and is no set to miss games against Everton , West Brom and Chelsea.
Manchester United boss Louis Van Gaal was hoping for a response following their shocking loss to Leicester City last Sunday.
A defensive crisis had forced the Dutchman to start with 19-year-old Paddy McNair in central defense and £27m summer signing Luke Shaw at left-back.
But despite their defensive deficiencies, they still had a vast array of attacking options and it did not take long for that to show.
Rafael raced down the right flank and delivered a cross which Rooney converted with a first-time glanced shot to the far post.
United almost ruined their attacking dominance when a poor back pass from midfield released Enner Valencia on the home goal only for the Ecuadorian to blaze his effort over.
United’s second came when Ander Herrera dispossessed Alex Song before Radamel Falcao slid a pass through to Van Persie, who angled in a right-foot shot.
Referee Lee Mason denied the Hammers a penalty when Morgan Amalfitano’s hooked across appeared to strike the arm of Falcao before the visitors pulled a goal back.
David De Gea missed punching away a corner and, after Valencia’s header came back off the crossbar, Sakho was on hand to nod home for his fourth goal in five games.
The sending off of Rooney f=gave the visitors some hope but, in the end, Van Gaal’s side secured the victory.
Manchester United manager Louis Van Gaal:
“The win is very important, you can imagine that. We played a very good first half with attractive football. We conceded again a goal from a set play.
“But OK, I am very happy that we hold the result until the end because it is very difficult to play against a team who not only have have one more player but who also play a lot of high balls. I am very pleased with the attitude of my players.”
On Rooney red card:
“It was a break out of a set play of ours and he makes a professional foul, I think you can call it like that. I don’t think Wayne wanted to do it that way but he did it and you can give a red card.”
West Ham boss Sam Allardyce:
“I’ve looked on the laptop and Kevin Nolan made a good run from deep and put the ball in the net. Unfortunately for us, the assistant saw something we didn’t.
“It’s unfortunate when you’ve worked so hard to get back in the game.
“We gifted Manchester United two goals and at 11 v 11 we had the best chances. Diafra Sakho could easily have had a hat-trick.”
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