Kenny Dalglish's team were determined to make Chelsea pay for the FA Cup Final defeat at Wembley last Saturday.
The home side attacked Chelsea from the start, a big change in approach from the weekend, and it paid off after 19 minutes when Luis Suarez ran into the box from the right and crossed the ball which Michael Essien deflected into his own net to give Liverpool the lead.
Six minutes later John Terry slipped to allow Jordan Henderson run through to score his second League goal of the Season with a crisp drive past Ross Turnbull.
Liverpool's Carroll and Suarez were tormenting the Chelsea rear-guard and Andy Carroll headed on a corner to Daniel Agger to head home his first Premier League goal of the Season on 29 minutes, to leave Liverpool 3-0 up after half an hour.
The Reds totally dominated the first half and should have made it four after Andy Carroll was fouled in the box by Ivanovic to concede a penalty.
Strangely, Stuart Downing stepped up to take the kick in injury-time, and he duly blasted the ball against the bottom of the upright with Turnbull going the other way.
The second-half began brightly, but it was Chelsea who scored with that man , Ramires scoring from a Chelsea corner to send a few shivers up Anfield spines on 50 mins.
However, Liverpool continued to charge forward and a disasterous kick by Chelsea goal-keeper Ross Turnbull fell to Johnjo Shelvey 30 yards out and he made no mistake with a great volley into an empty net for his first Premier League goal for Liverpool on 61 minutes making it 4-1 to the home-team.
Liverpool continued to make all the running defending well, dominating midfield and putting the Chelsea defence under all sorts of pressure refusing to their opponents a chance to get back into the game.
Kenny Dalglish made two substitutions in the 83rd minute; Kuyt replaced Downing and young Raheem Sterling came on for Maxi, who graciously waved goodbye to the croud as he came off, the Argentine showing that he will be moving on at the end of the season.
17 year-old Sterling nearly came up with his dream-goal but his snap-shot flew high and wide.
There was still time for Andy Carroll to get the goal his all-round display deserved, but he shinned a great cross by Glen Johnson wide.
So, 4-1 it ended infront of the Anfield crowd and even though we are only eighth in the League, it is nice to be able to report on a great performance by Liverpool!