* Chelsea boss under pressure after 3-1 home defeat
* Leaders Manchester City score late to beat Norwich 2-1
* Arsenal keep pace with impressive 3-0 win at Swansea (Adds late games)
By Martyn Herman
LONDON, Oct 31 (Reuters) - Jose Mourinho’s future as Chelsea manager looked increasingly uncertain after Liverpool beat them 3-1 in the Premier League on Saturday, with Philippe Coutinho scoring twice at Stamford Bridge.
Champions Chelsea’s third home league defeat of the season left them in 15th place in the table with 11 points from 11 games -- the worst ever start to a season by the reigning champions.
Manchester City needed a late Yaya Toure penalty to beat Norwich City 2-1 and retain top spot on goal difference from Arsenal who routed Swansea City 3-0 away.
Leicester City are up to third thanks to a 3-2 victory at West Bromwich Albion where they trailed, with Jamie Vardy scoring for the eighth Premier League match in a row.
Manchester United dropped to fourth after a 0-0 stalemate at Crystal Palace.
Chelsea’s hopes of retaining the title look forlorn with six league defeats already and Liverpool’s fans, celebrating a first league win for new manager Juergen Klopp, taunted Mourinho with chants of “You’re getting sacked in the morning”.
Former Chelsea midfielder Pat Nevin summed up the mood, saying: ”The questions over Mourinho will be a cacophony now.
“It’s not just the defeat but the manner of it. They were absolutely outplayed,” he added on BBC radio.
Yet the day had started so well for Chelsea.
There were only four minutes on the clock when Cesar Azpilicueta was given too much time and his cross picked out Ramires who headed powerfully into Liverpool’s net.
If the home fans expected that boost to fuel their side with new-found confidence, though, they were disappointed as a hard-working Liverpool side recovered to dominate possession.
Coutinho cleverly worked himself some space two minutes and 40 seconds into first-half stoppage time and curled a precise shot past Chelsea keeper Asmir Begovic.
Liverpool midfielder Lucas was lucky to avoid a second yellow card midway through the second half for a foul on Ramires -- a decision that infuriated Mourinho.
To rub salt into the wounds, Liverpool went in front a few minutes later when Christian Benteke’s knock down fell to Coutinho who again beat Begovic with a shot that brushed off John Terry, captaining Chelsea for the 550th time.
With Liverpool in complete control Benteke made the points safe with a low shot seven minutes from time.
Mourinho was clearly angry that decisions had gone against his side, explaining to the BBC: ”In the second half something happened that didn’t allow us to win the game.
Asked if he could turn around Chelsea’s unravelling season, he said simply: “If they allow us.”
Klopp was sympathetic, telling a news conference: “I feel for him. He’s a great coach. I don’t think anyone in this room doubts he’s one of the best in the world. Things like this happen. I had a similar situation at (Borussia) Dortmund last year.”
While Chelsea lurch from crisis to crisis -- they have lost nine times in all competitions including their midweek defeat on penalties by Stoke City in the League Cup which they won last season -- Liverpool are buoyant.
They are on 17 points and have moved up to seventh.
Fifth-placed West Ham United lost 2-0 at Watford, their first away loss of the season, while Newcastle United stayed in the bottom three after a 0-0 draw at home to Stoke City. (Reporting by Martyn Herman; Editing by Ken Ferris; and Clare Fallon)