Matic, meanwhile, was authoritative on his league debut for United following his recent departure from Chelsea, which looks increasingly like an ill-judged decision from the champions. He created the first goal by dispossessing West Ham's Pedro Obiang and sparking the break, and proved to be an impenetrable shield in front of United's back four.
He could be one of the signings of the summer at 40 million pounds.
Anthony Martial and Paul Pogba scored in the final three minutes of normal time to leave United top of the early standings.
Earlier, Tottenham beat 10-man Newcastle 2-0 away thanks to goals by Dele Alli and Ben Davies, with last season's runner-up only pulling clear at St. James' Park after Jonjo Shelvey's 48th-minute red card.
Shelvey was sent off for treading on the foot of Alli, an act that was even more foolish as it took place right in front of the referee.
Spurs are the only team in the Premier League not to make a signing this summer but they are still looking likely title contenders, alongside United.
- AP