Juan Mata missed a fine chance to equalise for the Reds two minutes after half-time, blasting the ball over the bar after fine work by Andreas Pereira, but then United, already short of strikers, lost Marcus Rashford to a groin injury.
West Ham then made the points safe when Aaron Cresswell scored, sending a free-kick sailing into the top corner from the edge of the box.
Ten man Arsenal produced a stirring comeback to beat Aston Villa 3 -2 at the Emirates.
Arsenal had an early chance when Ainsley Maitland Niles blazed over, but then the right-back picked up an early booking as the home side were pressed back. And then Villa took the lead when Anwar El-Ghazi crossed and John McGinn was allowed to stroll through the home defence and score with a left-foot shot. Matters then got worse when Maitland-Niles picked up another booking 5 minutes before half-time, and was shown a red card.
Forced into a defensive re-shuffle at half-time, Arsenal sacrificed teenager Bukayo Sako for Calum Chambers, but it was Villa who had most of the chances until they conceded a penalty, Björn Engles with the trip inside his own box. Nicolas Pépé stepped up and drilled the ball down the middle for his first Arsenal goal.
They were level for just a minute, Wesley putting Villa back in front after fine work from Jack Grealish down the left. Matteo Guendouzi then hit the post for the home side with a long range effort but then they did pull level from an unlikely source, Chambers finding the top of the net from inside the box. The comeback was then complete when Pierre-Emerick Aubameyang found the net with a right-foot shot from a free-kick. Villa pressed hard for an equaliser, but the Gunners held fast.
Liverpool preserved their 100% record by winning 2 – 1 at Chelsea, maintaining their five point lead at the top of the table. Liverpool took the lead in the 14th minute when Andreas Christensen was harshly adjudged to have brought down Sadio Mané on the edge of the box. Mo Salah back heeled the ball to Trent Alexander Arnold, and he blasted the ball into the top corner.
Chelsea had a great chance to equalise when Tammy Abraham was played through, but Adrian, in the Liverpool goal saved with his legs. Then they did get the ball in the net through captain Cesar Azpilicueta, after Willian broke down the left only for VAR to rule it out for offside earlier in the move.
Liverpool almost immediately punished them, Roberto Firmino left unchallenged to head home from a corner. And soon after half-time Firmino almost scored again when he was left free at the back post, only for Kepa in the Chelsea goal to make a fine diving stop.