Arsenal bounced back from two successive Premier League defeats in emphatic style by thrashing Wigan Athletic 4-0 at the Emirates on Saturday.
Aston Villa also gained ground on the leaders with a 2-0 home win over Portsmouth, who are still without a point after six games.
Promoted Burnley's good start continued when they beat Sunderland 3-1 with two goals on debut from on-loan striker David Nugent, Birmingham City beat Hull City 1-0 away while Bolton Wanderers and Stoke City drew 1-1.
Villa's win takes them up to 12 points - along with Tottenham Hotspur, Manchester City and Manchester United - with Chelsea leading the way with a maximum 15 points from five games.
Liverpool, who have nine points, visit West Ham United later on Saturday while there are four games on Sunday, including the Manchester derby and Chelsea against Tottenham Hotspur at Stamford Bridge.
IMPERIOUS BEST
After their two fruitless trips to Manchester, Arsenal began the day nine points behind Chelsea, albeit from a game less, but were back to their imperious best on home soil.
Their early control was rewarded after 25 minutes when Vermaelen headed in a Robin van Persie corner.
Eboue missed a good chance for a second 10 minutes later while Van Persie also went close in first half injury time.
Vermaelen, already looking an astute summer signing after joining from Ajax Amsterdam for a reported 10 million pounds ($16.35 million), showed the way with a superbly taken left footed curler four minutes into the second half.
Eboue got the third on the hour when he diverted an Eduardo Da Silva shot after the Croatian's initial effort came back from a post.
Wigan barely threatened until a late goal by substitute Paul Scharner was ruled out for offside.
Fabregas, limping heavily, backheeled the fourth in the last minute to take Arsenal's goal tally to 17 in five league games - only three of them wins.
Villa were similarly untroubled against a toothless Portsmouth and hardly had to break stride to secure a straightforward win.
James Milner put them ahead with a penalty after 34 minutes and Gabriel Agbonlahor cashed in on more sloppy defending to shoot the second from the edge of the box at the end of the first half.
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