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By Martyn Herman
LONDON, Dec 1 (Reuters) - Chelsea and Manchester City offered compelling evidence that they will lead the pursuit of leaders Arsenal and champions Manchester United lost further ground on a Sunday that brought the third managerial casualty of the Premier League season.
Jose Mourinho's Chelsea recovered from conceding a goal after 13 seconds at home to Southampton, scoring three times in the second half to win 3-1 and close the gap on Arsenal to four points with a third of the season gone.
Free-scoring Man City are third, two points further adrift, after spanking Swansea City 3-0 to take their home goal tally to 16 in their last three games.
Wayne Rooney equalised twice for United in a 2-2 draw at Tottenham Hotspur which left them nine points off the pace and Liverpool, who began the day in second, endured a miserable afternoon, going down 3-1 at Hull City and hearing that striker Daniel Sturridge will be out for around eight weeks.
Struggling Fulham predictably sacked Martin Jol and Tottenham manager Andre Villas-Boas, himself in the media spotlight after his team's faltering form, showed the strain with a rant at his post-match news conference.
For the third time this season in the top flight a goal went in after 13 seconds with Jay Rodriguez taking advantage of a Michael Essien error to give Southampton a shock lead at Chelsea.
There was little evidence in the opening half that Chelsea could avoid a first ever home league defeat under Mourinho but they overwhelmed high-flying Southampton after the break.
Defender Gary Cahill equalised on 55 minutes after John Terry's header had been diverted against the post.
Seven minutes later Terry celebrated his 400th Premier League appearance with a towering header before striker Demba Ba rounded off the victory with a late third.
"In this crazy league this result is important as once again title contenders have dropped points," Mourinho said.
City were not quite as rampant as they were in a 7-0 win over Norwich and a 6-0 drubbing of Tottenham last week but they were too strong for a Swansea side missing leading strikers Michu and Wilfried Bony.
Alvaro Negredo curled in an eighth-minute free kick to give City the lead, although they had to wait until the second half to secure the points through Nasri's brace.
"I'm pleased because we won against a very difficult team, especially when they had possession," City boss Manuel Pellegrini said.
"We didn't play very well in the first half but in the second we scored two goals and had more chances."
City's task is to emulate their home form on the road where they have been woeful, starting at West Bromwich Albion on Wednesday when Chelsea go to Sunderland and Arsenal host Hull.
Under pressure Spurs boss Villas-Boas accused reporters of having an agenda against after his side's draw with United, a verbal spat that overshadowed an improved showing by his side after their humiliation at Man City.
Kyle Walker fired Spurs in front after 18 minutes with a free kick that went under United's four-man wall but Rooney showcased his poacher's instinct to level after 32 following a dreadful mistake by Walker.
Sandro's thunderbolt restored Tottenham's lead after the break but when Hugo Lloris was adjudged to have brought down Danny Welbeck in the area Rooney strode up to thump his side level with his eighth league goal of the campaign.
Even so, United manager David Moyes said he was concerned that the gap to Arsenal was growing.
"It's a busy period coming up and we want to be on the shirt tails of (the leading teams) going into the end of the year, and at the start of next year," Moyes said.
"Undoubtedly Arsenal have been very consistent and they have got off to a great start but there will be a lot of teams now looking to chase them down and hopefully we are one of them."
Villas-Boas, whose side remained ninth but only three points off the top four, praised his side but spent most of his news conference arguing with a journalist.
"People insult by integrity, my human values, my professionalism and one of these people is sitting here," said the Portuguese who was apparently also riled by former chairman and host of TV show "The Apprentice" Alan Sugar's midweek Twitter comments saying Spurs should hire Alex Ferguson as manager.
Hull, who had never beaten Liverpool, opened the scoring on 20 minutes thanks to a huge slice of good fortune, Jake Livermore's shot from distance cannoning off the boot of Martin Skrtel and looping over keeper Simon Mignolet.
Liverpool levelled thanks to a curling free kick from Steven Gerrard but their lacklustre performance was punished in the second half when David Meyler latched on to a loose ball and buried it into the bottom corner.
Skrtel deflected in a Tom Huddlestone shot with three minutes remaining to wrap up the points for Hull.
(Editing by Ed Osmond)