Cardiff City picked up a vital win against West Bromwich Albion, West Ham United and Sunderland were both frustrated in a goalless draw, Newcastle United's clash with Southampton ended 1-1 and Hull City's home clash with Stoke City ended 0-0.
Manchester City made it eight wins out of eight on home soil as they produced another devastating display of attacking football to beat title rivals Arsenal 6-3 in an extraordinary game at the Etihad Stadium.
Sergio Aguero showed expert technique to volley City ahead in the 14th minute after Martin Demichelis had flicked on a corner, before Arsenal grabbed an unexpected equaliser when Theo Walcott's scuffed shot left Costel Pantilimon rooted to the spot.
Alvaro Negredo tucked in Pablo Zabaleta's cross after a sweeping move to make it 2-1 to City in the 39th minute, as Laurent Koscielny suffered an injury in trying to prevent the goal and had to be stretchered off.
An Arsenal mistake presented Fernandinho with the chance to put City further in front on 50 minutes, but Arsenal stayed in contention as Walcott curled in a wonderful strike for his second of the match.
The Gunners continued to look dangerous but it was City who always had the edge in a pulsating contest and David Silva side-footed home from close range in the 66th minute to restore their two-goal lead and the excellent Fernandinho clipped the ball over Wojciech Szczesny to give Manuel Pellegrini's side a fifth.
Per Mertesacker headed home a consolation for the visitors deep into injury time but there was still time for a sixth for City as James Milner was tripped in the box by Szczesny to allow Yaya Toure to slide home a penalty.
Chelsea made the most of Arsenal's defeat to narrow the gap at the top to two points, but they were made to work hard in a 2-1 victory over Crystal Palace.
Fernando Torres broke the deadlock in the 16h minute as he reacted quickly to fire a rebound past Julian Speroni after Willian had struck the post with a low shot from distance.
Marouane Chamakh continued his recent revival by steering in a volley from Joel Ward's cross to equalise for Palace just before the half-hour mark, but Chelsea quickly restored their lead as Ramires picked up the ball from Eden Hazard and slammed powerfully into the top corner from 20 yards.
Palace kept fighting hard in the second half in a bid to get back into the game, but the Blues held firm to stay one point ahead of third-placed City.
Everton are another point further back in fourth after seeing off Fulham 4-1 at Goodison Park.
Roberto Martinez had challenged his players to maintain their standards after fine performances against Manchester United and Arsenal, and Leon Osman opened the scoring with a terrific finish from the edge of the area after receiving a pass from Steven Pienaar.
Alexander Kacaniklic missed a glorious opportunity to equalise but was later brought down by Gareth Barry in the box after 67 minutes and Dimitar Berbatov stepped up to score the penalty for Fulham and make it 1-1.
However, Seamus Coleman put Everton back in front in the 73rd minute after Fulham failed to deal with a Pienaar cross, and Barry then headed in from close range with five minutes remaining after a scramble in the area.
Kevin Mirallas added a late fourth with a long-range strike which should have been kept out by Maarten Stekelenburg, as Fulham were kept in the bottom three.
Newcastle and Southampton played out a 1-1 draw at St James' Park following an absorbing encounter between two teams flying high so far this season.
The Magpies were gifted a goal in the 27th minute as Jos Hooiveld failed to connect with the ball for what should have been a straightforward clearance, allowing Yoan Gouffran to skip round Paulo Gazzaniga.
Southampton responded to the setback by making a double change at half-time and one of the substitutes, Adam Lallana, helped set up the equaliser on 65 minutes by flicking the ball on to Jay Rodriguez, who played a slick one-two with Steven Davis before firing into the bottom corner.
Loic Remy spurned a great chance to restore Newcastle's advantage as he shot horribly off target with just the keeper to beat, while there was a bizarre late incident when referee Mike Jones was knocked to the ground by an accidental punch from Moussa Sissoko, who received no punishment.
The crucial battle at the bottom of the table at Upton Park ended goalless as West Ham and Sunderalnd had to settle for a point apiece.
Phil Bardsley rattled the crossbar in the first half and it was Sunderland who created the better chances, but they could not land find a winner and the result leaves them four points adrift at the bottom.
Cardiff claimed an important 1-0 victory at home to West Brom to pull four points clear of the relegation zone and increase the pressure on the Baggies.
Both teams have been struggling for form in the past few weeks and it was a scrappy first half at the Cardiff City Stadium with chances few and far between.
Conditions were difficult with torrential rain driving down but Cardiff kept battling and were rewarded in the 65th minute when Peter Whittingham guided a header home from Craig Noone's cross.
The day's late game ended goalless as Hull City and Stoke City shared the points at the KC Stadium.
Both sides had chances to win in the second half but the two goalkeepers excelled themselves, with Asmir Begovic clawing away an Ahmed Elmohamady header and Allan McGregor brilliantly denying Peter Crouch.
Stephen Ireland had a goal disallowed for offside and Ryan Shawcross also headed against the crossbar as Stoke finished strongly, but Hull clung on for a draw.