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West Ham United 2 Leicester City 0
Andy Carroll was on target as West Ham's fourth win in five games ensured Leicester would be bottom of the Barclays Premier League at Christmas.
Only twice before - West Brom in 2004-2005 and Sunderland last season - have the side at the foot of the Premier League standings on December 25 avoided relegation.
The Foxes were culpable as their winless run was extended to 12 games through goals from Carroll and Stewart Downing in the Hammers' 2-0 win.
Paul Konchesky, Barking-born and playing against his old club, presented Carroll with the opening goal moments after the Hammers striker had missed a straightforward opportunity.
But there was little Leicester could do to stop Downing's strike as the playmaker curled a sumptuous shot into the far corner.
Adrian saved well to deny Foxes substitutes David Nugent and Leonardo Ulloa late on as West Ham kept a cleansheet in a comfortable win.
The fourth-placed Hammers have made their best Premier League start and now have an eye on Europe - home fans celebrated the win by singing "Barcelona, we're coming for you" - while Leicester must dig deep to have any hope of survival.
Leicester's only wins this term were over Stoke and Manchester United in successive games in September and they next play Tottenham on Boxing Day.
The Hammers play at Chelsea, whose manager Jose Mourinho accused them of playing "football from the 19th century" in January's goalless draw between the sides.
How Mourinho's opinion must have changed as Allardyce has delivered a stylish side, driven forward by Alex Song and Downing, with Carroll and Diafra Sakho providing contrasting threats up front.
Leicester manager Nigel Pearson was fined £10,000 and given a one-match touchline ban following his altercation with a fan during last month's loss to Liverpool, but his troubles are deeper than that.
Pearson, who usually sits in the stands anyway, saw his team subjected to an early bombardment, with Sakho slicing wide from Kevin Nolan's pass.
The Foxes boss watched Jamie Vardy's dangerous cross into the six-yard box evade everyone and his side fail to capitalise on Adrian's throw straight to Esteban Cambiasso.
Sakho should have given West Ham the lead and then his strike partner spurned a far easier chance on receipt of Downing's cut-back. From eight yards out, Carroll blasted over.
The striker swiftly made amends after West Ham cleared long to the left wing.
Konchesky, from just inside his own half, aimlessly passed back into no-man's land.
Carroll burst on to the ball and neatly lifted it over goalkeeper Ben Hamer for his third goal of the season.
Riyad Mahrez forced Adrian into a sharp save, but the Hammers were dominant, with Leicester's frustration clear.
Song required treatment for one heavy challenge and returned to the field be felled by Vardy, who was booked.
Carroll was unable to connect with an acrobatic attempt early in the second half and there was a moment of alarm when he turned his ankle and fell into the brick-walled photographers' pit by the touchline. The England striker shrugged off the incident to resume.
The direct route led to West Ham's second, but Carroll was not involved as Sakho headed down to Downing, who struck a delightful curling shot beyond Hamer.
Pearson, who is awaiting the written reasons for his punishment before deciding his options, appeared in the technical area to bellow at his players, but it had little impact.
There was concern for West Ham as James Tomkins walked off gingerly when replaced by James Collins, who was beaten by Nugent only for the striker to fire over.
Nugent and Ulloa were denied by Adrian at point-blank range late on as Leicester rallied.
Had either header gone in, it would have set up a tense finale, but as it was the Hammers eased to victory.