* Chelsea boss under pressure after 3-1 home defeat
* Leaders Manchester City score late to beat Norwich 2-1
* Arsenal keep pace with emphatic 3-0 win at Swansea
By Martyn Herman
LONDON, Oct 31 (Reuters) - Jose Mourinho's future as Chelsea manager looked increasingly insecure after a 3-1 defeat by Liverpool on Saturday, Philippe Coutinho scoring twice at Stamford Bridge as the champions lost a sixth Premier League game in 11.
Chelsea's third home league reverse 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.
They are already 14 points behind Manchester City who needed a last-gasp Yaya Toure penalty to beat Norwich City 2-1 and retain top spot on goal difference from Arsenal who won 3-0 at Swansea.
Toure's spot kick spared the blushes of City keeper Joe Hart who fumbled a routine catch to gift Norwich a late equaliser.
All Arsenal's goals came after the break as they made it five league wins in succession -- Olivier Giroud, Laurent Koscielny and Joel Campbell all on target.
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 league match in a row.
Manchester United dropped to fourth after a 0-0 stalemate at Crystal Palace, their second successive goalless league draw.
Chelsea, labouring in the Champions League, out of the League Cup and as good as finished in the title race, are in free fall 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 winger 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.
Triple Premier League winner Mourinho was tight-lipped afterwards, but asked if it could have been his last game in charge, he said: "No".
The day had started so well for Chelsea.
There were only four minutes on the clock when Cesar Azpilicueta's was headed in by Ramires.
If the home fans expected Chelsea to force home their advantage, though, they were disappointed as a hard-working Liverpool side recovered to dominate possession.
Coutinho equalised two minutes and 40 seconds into the indicated two minutes of first-half stoppage time, curling 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 Coutinho again beat Begovic with a shot that brushed off John Terry, captaining Chelsea for the 550th time.
Christian Benteke made the points safe with a low shot seven minutes from time.
"What happened in the second half was a consequence of crucial moments, moments that the stadium saw, and more than just see it, the players felt it. From then what happened was just a consequence," Mourinho told reporters.
Asked if he could turn around Chelsea's unravelling season, he said cryptically: "If they allow us."
Klopp was sympathetic. "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," the German said.
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 after a run of six matches unbeaten in the league.
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)