But they made hard work of their victory with the three points not safely in their grasp until two late goals finally won them a game they should have wrapped up much earlier, such was their domination.
Charlton got off to a disastrous start giving away a penalty after just three minutes.
The culprit was former Liverpool player Djimi Traore who was back in the home side after injury. His foot was high as Jermaine Pennant went to head the ball and referee Howard Webb pointed to the spot. Xabi Alonso put the penalty kick into the net to give the visitors the lead.
The Premiership strugglers could not have picked a worse time to play Liverpool who arrived at The Valley on a five-match run without conceding a goal.
The only glimmer of hope for Charlton was the fact that Liverpool had won only once away this season and had taken only five points from a possible 24 on their travels.
After conceding the early goal Charlton were all at sea and could have been three goals down in the first 15 minutes. Craig Bellamy was denied by a last-ditch tackle from Luke Young and Traore made some amends for his earlier mistake when he cleared off the line from Pennant.
Charlton saw a shaft of light when Jimmy Floyd-Hasselbaink's goalbound effort was deflected for a corner. The home side missed a great chance when Andy Reid broke clear to fire in a low angled shot which goalkeeper Jose Reina pushed out, and an off-balance Hermann Hreidarsson fired over the bar from the rebound.
Liverpool had scored first in seven games this season and gone on to win them all, so Charlton's hopes of getting something from the match looked unlikely. The visitors totally dominated midfield and had the home side on the back foot for long periods.
There was more bad news for Charlton at half-time when Reid failed to appear after the break and they also lost skipper Young midway through the second half.
Liverpool should have put the game out of Charlton's reach with a second goal but they continued to squander opportunities as Addicks keeper Thomas Myhre saved well from Alonso and Steven Gerrard.
Liverpool's domination was embarrassing for the home side and yet another chance went begging when Dirk Kuyt thumped his shot against the post.
Charlton had a rare goalscoring opportunity when substitute Darren Ambrose volleyed over the bar and they missed an even better opportunity when Darren Bent screwed his shot across the face of the goal.
Eventually the expected sting in the tail came from Liverpool with two late goals, Bellamy hooking in an angled shot after Charlton had waited for an offside flag, and Gerrard put the icing on the cake with an exquisite finish to finally shatter Charlton's meek resistance.
The Londoners plight in the relegation zone is looking increasingly hopeless and they have taken just 12 points out of a possible 54.
Liverpool, on the other hand, have scored 11 goals in their last three matches and haven't conceded in six. But they may have left their title challenge too late after their stuttering start to the season left them in the slipstream of leaders Manchester United and Chelsea.