The Londoners leapfrog the Scousers and are now two points behind leaders Manchester United.
Both goals came in the second hald which finally saw off defence-minded Middlesbrough at Stamford Bridge.
The home side completely dominated the game from start to finish.
Ashley Cole almost opened his season's account on 12 minutes by darting to the far post to meet Jose Bosingwa's right-wing cross. Unfortunately for the left-back his header smacked against the side-netting.
Michael Ballack's curling 20-yard free-kick then zipped off the greasy surface on 15 minutes but Ross Turnbull got his body behind it and parried the ball to safety.
The visitors' first attempt on goal came on 22 minutes when a powerful Stewart Downing free-kick was blocked by Alex.
Until that point Boro had struggled to get out of their own half, such was Chelsea's dominance of possession.
Didier Drogba was brought on at half-time for the luckless Florent Malouda and the Ivory Coast striker was clean through within a minute but scuffed his right-footer wide of Turnbull's right post.
Kalou had a glorious chance to put the home side ahead on 55 minutes but somehow managed to clip a header from six yards out over the bar when it was easier to nod it past Turnbull.
But he made amends three minutes later when, from Frank Lampard's corner, the ball fell to Alex whose header was cleared into the path of Kalou by defender David Wheater and the striker hit a sweet right-footed volley cleanly into the net from just inside the penalty area.
Boro boss Gareth Southgate rang the changes bringing on Afonso Alves and Tuncay for Marlon King and the ineffectual Mohamed Shawky on 64 minutes.
A quick breakaway from Chelsea five minutes later saw Nicolas Anelka race into the Boro penalty area on the right and send in a low pass to Lampard who bizarrely attempted to slide the ball in with his left foot instead of his natural right and the ball clipped off the foot and away to safety.
Chelsea scored their second on 81 minutes when Kalou rose, unmarked, from Lampard's left-sided corner. Turnbull came out for the ball but missed it and the Ivory Coast striker headed home into an empty net from six yards out.
Chelsea boss Luiz Felipe Scolari rewarded Kalou for his brace by immediately substituting him for Deco but the Blues eased their way through the final minutes to record three vital points.