The Blues, who could have gone top with a win, struggled to get out of first gear throughout but did give themselves hope when Diego Costa pulled one back on the hour after a sloppy start saw them fall two behind.
First-half strikes from Dejan Lovren and Jordan Henderson, the latter a real contender for Goal of the Season, proved to be enough for Liverpool to claim all three points, however, ending Antonio Conte's unbeaten run in the process for a below-par Chelsea.
It took less than two minutes for Liverpool to fire away their first attempt on target, as Daniel Sturridge picked up the ball on the edge of the box and sent a shot down the middle which squirmed under Thibaut Courtois's body but not quite over the line.
As the game settled down it was the Reds who were taking control of things, putting together some positive attacking moves and being rewarded 17 minutes in when Lovren crept in at the back post to open the scoring.
The Croatia international, who was back in the team along with Philippe Coutinho in the only two changes from last time out, found himself completely unmarked along with three other teammates and was able to blast home first time past the reach of Courtois.
In a complete reversal to the Blues' opening 45 minutes at Swansea City last weekend - a match they would fail to win in the end - the Blues struggled to get going and could have been two down when former player Sturridge worked his way into the box and sent a shot across the face of goal.
That did not act as a warning sign, though, as Henderson's belter from more than 30 yards out ended right in the top corner soon after.
Chelsea failed to truly test Simon Mignolet on a single occasion in a poor first-half showing, with the closest they came to a breakthrough arriving shortly before the interval when Branislav Ivanovic flicked on a cross into the hands of Liverpool's well-positioned keeper.
A more aggressive approach was adopted by the West London outfit in the second half in terms of getting the ball forward in a quicker manner, though Conte surprisingly opted against making any half-time alterations.
Conte kept things the same in a flat opening 15 minutes of the second half, and his faith paid off on the hour when Nemanja Matic stood the ball up for Costa when reaching the byline for the Spaniard to easily tuck away his fifth of the season - the only positive moment on the night from a Blues' perspective.
The tide looked as though it was about to turn at that point; Costa only being denied a leveller by a Mignolet save after getting on the end of Oscar's knockdown in what turned out to be a second half devoid of any major chances.
It took until 10 minutes from time before the next on-target shot of the half arrived, but Courtois was across brilliantly to deny compatriot Divock Origi who could not find the net with his header from five yards out.
That at last sparked some action from Conte, who made all three subs at once with time fast ticking down in an attempt to keep his unbeaten start to life at Stamford Bridge intact.
Conte had won each of his last 21 home league outings prior to tonight, but Chelsea did little to truly trouble their opponents in the remainder of the match to make it back-to-back wins at Stamford Bridge for the Reds.body check tags ::