Arjen Robben scored his second winning goal in as many games and Chelsea FC reached the Premiership summit for the first time this season as champions Arsenal FC surprisingly dropped points.
Having hit the only goal at PFC CSKA Moskva in midweek to send Chelsea into the knockout stages of the UEFA Champions League, the Dutch winger scored in the 72nd minute to take José Mourinho's side two points clear at the top of the table.
Everton underlined their status as the Premiership's surprise package with a positive opening, in which Steve Watson could have opened the scoring inside 40 seconds. By the time Tim Cahill had brought a superb diving save out of Petr Cech, Chelsea themselves had gone close through Frank Lampard after a rare slip from Alessandro Pistone.
Robben produced the moment of the first half in the 23rd minute, brilliantly flicking the ball over David Weir and sending in a fine half-volley which Nigel Martyn tipped on to the crossbar with a spectacular save. Everton's best chance arrived in the 57th minute as a well-worked short corner eventually found Alan Stubbs in space near the penalty spot, but the defender could only direct his header wide.
The visitors were made to pay 18 minutes from time following a great ball over the Everton defence from Eidur Gudjohnsen which allowed Robben to burst forward from the halfway line, hold off Weir and, despite the defender's attentions, prod past Martyn for the winning goal.
Arsenal, meanwhile, failed to win for the third successive league match as they were held to a 1-1 draw at Crystal Palace FC. Thierry Henry struck first for Arsenal after 63 minutes but two minutes later Finnish international Aki Riihilahti replied to give the home team an impressive point.
Liverpool FC's perfect home record came to an end against Birmingham City FC as Darren Anderton latched on to a Matthew Upson header to score his first goal for the club and give the visitors all three points at Anfield. Managerless Tottenham Hotspur FC, meanwhile, lost 3-2 at home to Charlton Athletic FC, Shaun Bartlett scoring twice and Jerome Thomas once to make it 3-0 after 50 minutes. Tottenham responded with late goals from Robbie Keane and Jermain Defoe.
Norwich City FC remained without a league victory after a 1-1 draw with Blackburn Rovers FC, for whom Paul Dickov levelled with four minutes left. Southampton FC denied West Bromwich Albion FC an away success thanks to an 86th-minute strike from Anders Svensson, while Aston Villa FC beat Portsmouth FC 3-0 with first-half efforts from Peter Whittingham, Juan Pablo Angel and Nolberto Solano.
Additional reporting by Jonathan Caswell
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