Jonathan Woodgate headed the opener on the half hour and teenager James Milner, on for the injured Harry Kewell, added a second on the chime of half-time.
The 16-year-old ace, the youngest player to score in the Premiership, followed up his strike in the Boxing Day win over Sunderland with another as Leeds moved into the safety of mid-table.
Claudio Ranieri will be disappointed to have missed the chance to close the gap on leaders Arsenal, who they face on New Year's Day.
Manchester United got back on the winning trail after two successive defeats with a 2-0 victory over Birmingham at Old Trafford.
Sir Alex Ferguson brought the big-guns back in the form of David Beckham and Rio Ferdinand.
It had the desired effect as Diego Forlan swooped on a Beckham knock-down after 37 minutes to break a resilient Blues rearguard.
Birmingham had chances to level the score but Clinton Morrison and Jovan Kirovski, a former Manchester United trainee, both missed chances.
Beckham made them pay the ultimate price with 73 minutes on the clock latching onto an inch perfect pass from Juan Sebastian Veron to float cleverly into the net.
United remain in third, despite Chelsea's defeat, four points behind Arsenal at the top.
Aston Villa edged away from the relegation dog-fight with a slender 1-0 win over Middlesbrough at Villa Park.
Dion Dublin bagged his 200th career goal on 11 minutes and the sending off of Boro's Mark Wilson on the half hour, for two bookable offences, put Villa firmly in the driving seat.
Ten-man Boro could not get back into the game and their dismal away form continued in the Midlands.
Charlton compounded the misery of struggling West Brom with a Kevin Lisbie strike after just six minutes enough to take the spoils.
The gutsy Baggies threw everything at The Addicks at The Valley but could not find a leveller as Charlton held out for a 1-0 victory.
West Ham left it late to steal a valuable point in a thrilling 2-2 draw with Blackburn at Ewood Park.
Damien Duff put Rovers ahead with three minutes gone but The Hammers rallied and equalised on 24 minutes.
A Steve Lomas shot deflected off giant defender Martin Taylor and looped over the stranded Brad Friedel.
West Ham then shot themselves in the foot 12 minutes from time - not for the first time this season - with David 'Calamity' James throwing the ball into the path of Tugay, who received possession and gave it to Andy Cole.
The former Newcastle United and Manchester United man made no mistake scoring his 150th Premiership goal - second only to Alan Shearer.
Jermaine Defoe struck four minutes from time to grab a point but The Hammers still sit at the bottom of The Premiership heading into the New Year.
Southampton left it until the dying seconds to defeat Sunderland 2-1 at St Mary's Stadium.
James Beattie, who is pressing for an England call, continued his purple patch in front of goal heading home on 73 minutes - his 12th league goal of the season.
Substitute Tore Andre Flo levelled after 77 minutes for The Black Cats but that was not the end of the scoring as Jo Tessem struck deep into stoppage time.
Everton and Bolton both had their chances to take the spoils but had to settle for a point apiece at Goodison Park in a scoreless draw.
The best chances fell to hot-shot Wayne Rooney who hit the crossbar on the hour mark, while Jay Jay Okocha also rattled the woodwork with 10 minutes remaining.
Man City continued their surge up the table with a 1-0 triumph over Fulham at Loftus Road.
Nicolas Anelka had gone close on a number of occasions for The Citizens and finally got his name on the score-sheet six minutes from time to clinch all three points and leave Fulham nervously looking down the table.
For the match summaries click below
Aston Villa v Middlesbrough
Blackburn v West Ham
Charlton v West Brom
Everton v Bolton
Fulham v Man City
Leeds v Chelsea
Man Utd v Birmingham
Southampton v Sunderland
For the Premiership table click here
