Rampant Liverpool turned up the heat on beleaguered West Ham boss Slaven Bilic with a 4-1 win on Saturday as former champions Leicester City extended their unbeaten run with a draw at Stoke.
Elsewhere, struggling West Brom's winless run stretched to nine league matches in a 1-0 loss against 10-man Huddersfield, cranking up the pressure on manager Tony Pulis, while Burnley's 1-0 victory at Southampton lifted them briefly to sixth in the table.
In the evening fixture at the London Stadium, Jurgen Klopp's Liverpool took the lead in the 21st minute following a lightning break when Mohamed Salah steered home following a pass from the returning Sadio Mane and doubled their lead within three minutes when Joel Matip tapped in after a corner.
Bilic brought on Andy Carroll for the second half and West Ham were back in the match 10 minutes later through Manuel Lanzini but as the home fans were still celebrating, Alex Oxlade-Chamberlain restored Liverpool's two-goal cushion and Salah put the game beyond the home side.
The victory took Liverpool back to sixth position after they were briefly dislodged by Sean Dyche's Burnley but it leaves West Ham just a point above the relegation places with a single win in the Premier League since early September.
A disappointed Bilic said his side had started well but then conceded two "cheap" goals.
"I have to talk to the chairman, we are going to discuss this defeat," he said. "It's not the first one, it's the second in a row in home. It is a very difficult situation for me. I always believe in myself, I wouldn't be here otherwise."
But Klopp was delighted with his team's display.
"The result, it feels good," he said. "We changed our approach, it was a counter-attacking line-up to use our speed from a deep situation. It was brilliant play for the first goal."
In the early game, former England striker Peter Crouch came off the bench to rescue a point for Stoke City in a 2-2 draw, denying new Leicester manager Claude Puel another victory after he won his first match at the helm against Everton last week.
The 2015-16 Premier League champions are now unbeaten in six games in all competitions after early season struggles but will be disappointed they twice let their lead slip, and in the end were indebted to goalkeeper Kasper Schmeichel, who made a fantastic flying stop in the dying seconds.
"I am happy with the attitude of my players, it was a good game, good intensity and passion," said Puel.
"We had a lot of chances today. It is difficult to accept one point but Kasper saved well at the end so then OK, we take a point."
Huddersfield's Rajiv van La Parra broke the deadlock at home to West Brom, lighting up a match devoid of real quality with a stunning strike on the stroke of the interval that lifts them up to 10th.
West Brom, struggling for goals, have not won a Premier League match since mid-August and remain just two points clear of the relegation zone, with Pulis's proud record of never being relegated under threat.
"We are in the results business and these results mean there's some pressure on me," said Pulis.
"I am disappointed professionally -- it hurts to go such a long time without winning a game," he added. "But things conspire against you at times and you don't get the breaks."
Dyche's Burnley added to their impressive away record with a 1-0 win at Southampton, courtesy of a late strike from substitute Sam Vokes.
With three wins and two draws, Burnley have already won more games and points on the road than they amassed in the whole of 2016-17.
Brighton earned three points at struggling Swansea with a first-half goal from Glenn Murray and a Steve Cook strike in added time gave Bournemouth a 1-0 win at Newcastle that lifted them out of the relegation zone.
On Sunday, leaders Manchester City host Arsenal while second-placed Manchester United travel to Chelsea.
Tottenham, on a high after their historic 3-1 Champions League win against Real Madrid, host bottom-placed Crystal Palace.