Successive home defeats to Everton and Newcastle United ramped up the pressure on manager David Moyes earlier this month, but there was no repeat on this occasion as United coasted to their fourth win in a row in all competitions.
Danny Welbeck gave the Premier League champions the lead in the 26th minute with his first league goal at Old Trafford in more than 14 months.
And the England forward turned provider 10 minutes later, setting up teenager Adnan Januzaj, who took his first home goal for the club with aplomb.
The second half never really got going, with United substitute Ashley Young providing the only highlight when he curled in his second goal in four days with 18 minutes left.
Carlton Cole beat the offside trap to race clear and slot through the legs of David De Gea eight minutes from time to pull one back for the visitors, but it was too little, too late.
The result was slightly soured for United as Welbeck limped off with what looked to be a muscle injury early in the second half.
United climbed to seventh in the table with their success, while West Ham – who looked sluggish after their 2-1 League Cup quarter-final win at Tottenham on Wednesday – remain 17th.
Wayne Rooney returned from a minor groin problem for United to partner Welbeck up front, but Nemanja Vidic (knock) and Marouane Fellaini (back) remained on the sidelines.
Spanish goalkeeper Adrian retained his place for West Ham, while striker Modibo Maiga was promoted after scoring the winner at White Hart Lane.
Still missing suspended captain Kevin Nolan, West Ham struggled to get a foothold in the game and only an excellent Adrian save denied Tom Cleverley from close range in the second minute.
Rooney then curled a free-kick over and Antonio Valencia forced a decent stop from Adrian, before United's pressure told.
A lovely flick from Welbeck released Rooney in space and he returned the pass as the former burst into the penalty box to fire past Adrian from a tight angle.
Adrian's positioning could have been questioned by manager Sam Allardyce, but the keeper was not the only one left with egg on his face after Januzaj strolled through West Ham's defence to double United's lead nine minutes before the break.
Januzaj and Welbeck linked before the 18-year-old sold James Collins a dummy, slid past him and curled in his first goal at Old Trafford.
Valencia blasted over just before half-time and four minutes after the break, Jonny Evans' towering header had to be turned wide by Mark Noble.
Collins went close with a header at the other end, but United were still dominant – Javier Hernandez only denied by the offside flag after scoring in the 68th minute.
Young finally sealed the result shortly after, capping a routine win for United by curling Rooney's pass into the top-right corner.
That meant Cole's late goal had little significance as United posted a comfortable victory.
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