Chelsea maintained their 100 per cent home record with a 3-0 win over Aston Villa at Stanford Bridge. Oscar, Diego Costa and Willian all getting on the score sheet for the Blues.
Southampton are three points back, after another impressive 2-1 win over QPR.
Grazianno Pelle and Ryan Bertrand on target for the Saints.
Wayne Rooney and Robin Van Persie helped Manchester United to a 2-1 home win over Sam Allardyce's West Ham.
It finished goalless between Sunderland and Swansea City.
Manchester City came away from the KC Stadium with a 4-2 win over Hull City.
Aguero, Lampard and a double from Edin Dzeko helped move City to within five points of Chelsea.
Crystal Palace moved into the top half of the table after beating Leicester City 2-0 at Selhurst Park.
Frazier Campbell and Mile Jedinak helping the Eagles to a big three points.
And there were two massive derby games on Saturday.
In north London, it ended Arsenal 1. Tottenham. Nacir Chadli gave Spurs the lead after 54 minutes, before Oxlade-Chamberlain scored to secure a point for the home side.
Steven Gerrard gave Liverpool a 65th minute lead in the Merseyside derby. But while it looked like the Reds had secured all three points, Phil Jagielka smashed home an equilizer in stoppage time.
And in the only Premier League game on Sunday, West Brom hammered Burnley 4-0.
Craig Dawson, Graham Dorrens and a double from Saido Berahino on target for the Brummies.
