Second-half goals from French duo Nicolas Anelka and substitute Florent Malouda settled an absorbing contest high on commitment but lacking in clearcut chances.
Chelsea, who suffered their first defeat of the season at Wigan last weekend before an unconvincing Champions League victory in Cyprus, moved to 21 points, two clear of champions Manchester United who drew 2-2 with Sunderland on Saturday.
"After this match I think we have resolved our problem, it was not a big problem," Chelsea manager Carlo Ancellotti, who had harsh words for his players in the past week, told reporters. "We carried out what we had prepared before the game and for that I'm happy."
Liverpool, who have now lost three league games compared with only two defeats last season, slipped out of the top four behind Arsenal who enjoyed a scintillating 6-2 home victory over Blackburn Rovers.
West Ham United needed a late equaliser to earn a 2-2 draw at home to 10-man Fulham but they remained in the relegation zone while Everton drew 1-1 at home with Stoke City.
Ancellotti demanded an improvement and he got it, although the Italian would have been concerned when Liverpool dominated the opening 10 minutes with crisp passing.
Liverpool, also needing a quick response after a shabby midweek Champions League defeat by Fiorentina, failed to test Chelsea's second-choice keeper Hilario until six minutes from halftime when Fernando Torres headed straight at the Portuguese.
Chelsea had taken a grip on proceedings by then with Michael Essien stamping his authority in midfield.
Anelka had Chelsea's first chance but could not direct a header past Jose Reina from an Essien cross and Michael Ballack headed wastefully over from a pinpoint Deco delivery.
Chelsea's opener after 60 minutes came from an unlikely source. The usually miserly Javier Mascherano squandered possession to Frank Lampard in the centre circle and the ball was moved quickly to Deco and on to Didier Drogba who crossed for Anelka to stab his third league goal of the season.
Liverpool searched for an equaliser and Torres scuffed their best chance wide before Chelsea sealed victory late on when Drogba squared for Malouda to finish from close range.
Asked if three defeats in eight league games had wrecked Liverpool's title challenge, manager Rafael Benitez pointed out that it was too many draws which cost his side last season.
"Maybe this time we will win more and draw less," he said. "It's a long race and it's important to keep calm. We will see in May."
While Chelsea, apart from one blip, have chugged along smoothly this season, Arsenal have provided most of the thrills and spills.
Six different players were on target for the Gunners on Sunday as they took their goal tally to 24 in seven league games with a display of attacking panache watched by the club's record goal scorer Thierry Henry.
The former darling of the Arsenal fans, who
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