Chelsea notched a sixth successive Premier League win as they beat Crystal Palace 2-0, while Leicester City beat Arsenal 2-0 to move into second place on Saturday.
Stuttering Tottenham Hotspur`s winless run continued as they were held to a draw at home to Sheffield United, leaving last year`s Champions League runners-up languishing in 12th place.
Leaders Liverpool take on champions Manchester City at Anfield on Sunday in the biggest game of the season so far.
At Turf Moor, Burnley crushed West Ham United 3-0 to pile the pressure on Hammers boss Manuel Pellegrini, but Everton`s Marco Silva finally found some cheer as his side won 2-1 at Southampton.
Newcastle United claimed a second successive win as they beat Bournemouth 2-1 to climb into mid-table.
After their breathless midweek 4-4 home draw with Ajax Amsterdam in the Champions League, Frank Lampard`s Chelsea side enjoyed a rather more straightforward day against Palace.
Chelsea laboured in the first half against a rugged Palace side, but Tammy Abraham put them ahead after the break with his 10th goal of the season before Christian Pulisic sealed victory with his fifth goal in three league games.
The return of midfield shield N`Golo Kante helped Chelsea keep their third clean sheet of the season and move above champions Manchester City, who face a seismic clash away at league leaders Liverpool on Sunday.
Lampard fielded the club`s youngest-ever Premier League line-up at kickoff, giving 19-year-old defender Reece James his first league start, and his trust in youth is paying off.
"I am proud of the squad that we have got, but I also realise it`s still a snapshot in what is the big picture which is the long-term future here," he said.
"We have got so much improvement to do because the gap was too big last year between us and the top two, and we want to try and close that."
The mood could not be more different across London at Tottenham.
Spurs were given a fortuitous lead after halftime by Son Heung-min, but George Baldock`s equaliser earned Sheffield United a 1-1 and extended their unbeaten run to five league games.
It was no more than United deserved after they had a David McGoldrick goal ruled out for a fractional offside after a VAR check that took almost four minutes to complete.
While Sheffield United sit proudly in the top six, Tottenham - Champions League finalists in June - are stuck in 12th spot, without a league win since September.
"The reality is that for different reasons we are not showing the performances that we expect," Tottenham manager Mauricio Pochettino said after the match.
Arsenal have now gone four games without a win after their defeat at the King Power stadium against a Leicester side that is looking every bit as effective as their 2016 title-winning squad.
Jamie Vardy and James Maddison struck second-half goals as Leicester piled yet more pressure on Arsenal`s struggling Spanish manager Unai Emery.
Premier League top scorer Vardy`s 11th goal of the season left his manager Brendan Rodgers` purring.
"He is up there with the very, very top strikers in European football with what he brings to a team, his pressing. We`ve allowed him to do essentially what he wants to do," he said.
West Ham`s early season form is a fading memory, meanwhile, and they have picked up one point from the last 15 on offer.
Burnley had lost their previous three games but dominated on Saturday after Ashley Barnes poked home in the 11th minute.
The hosts were denied a second in the 36th minute when Chris Wood`s header was ruled out by VAR, but Wood did make it 2-0 after a mistake by defender Fabian Balbuena.
West Ham`s misery was complete when keeper Roberto Jimenez punched Ashley Westwood`s corner into his own net.
"When you concede so many easy goals it does not help. I am concerned at the easy goals we are conceding," Pellegrini, whose side have careered down the table, said.
Goals by Tom Davies and Richarlison gave Everton their first away win of the season to leave Southampton stuck in the bottom three. Newcastle trailed at home to Bournemouth but goals by DeAndre Yedlin and Ciaran Clarke sealed a 2-1 win.