Luis Suarez took his Premier League tally to 15 goals for the season by scoring twice to help Liverpool ease to victory against Sunderland.
Watched by new Anfield signing Daniel Sturridge, Raheem Sterling's lobbed goal gave the Reds an early lead.
Suarez doubled Liverpool's advantage soon after, racing into the area before stabbing the ball home.
The Uruguayan then made it 3-0 early in the second half with a close-range strike from Steven Gerrard's pass.
"Liverpool were at it from the go and they took their chances. The second half was an exhibition and they are starting to look a good team. They still need to bring in some players though. The system that Liverpool try to play gives the players confidence. Some will not be good enough and they look better players than they are. Glen Johnson is excellent, Steven Gerrard is coming back to his best and they have Luis Suarez."
The win means Liverpool have recorded back-to-back league victories for the second time this season and moves them up to eighth in the table.
For Sunderland it was their second successive defeat following the 2-1 loss to Tottenham at the weekend and they remain 14th.
Liverpool's attacking display would have impressed Sturridge, who completed the formalities of his move from Chelsea in the hours before kick-off.
Despite a confident start by Sunderland, it was the home side who were the first to threaten in the 11th minute when Suarez was fouled just outside the area and Stewart Downing curled the resulting free-kick towards the near post, but keeper Simon Mignolet did well to push the ball behind for a corner.
Liverpool's opening goal came eight minutes later. Suarez brought a Gerrard pass under control before expertly lofting the ball over the defence to release Sterling and the young England winger showed great composure to draw out Mignolet before lobbing the ball into the net.
The Sunderland defence were struggling to deal with Liverpool's pacey attacks and the hosts took full advantage by adding a second in the 26th minute.
Gerrard knocked the ball forward for Suarez to chase down the right and, though the Uruguayan was fouled by Carlos Cuellar, he stayed on his feet to charge towards goal and power a neat finish beyond Mignolet.
Suarez at the double
Luis Suarez's two goals against Sunderland marked his first back-to-back Premier League double, after also scoring twice against QPR
Despite the two-goal deficit, Sunderland still carried a threat when they got forward and they had a great chance to pull a goal back when Adam Johnson's deep cross found Matthew Kilgallon inside the area, but the defender's half volley was superbly denied by Pepe Reina.
Sterling and Suarez continued to combine well and cause Sunderland problems after the break, and a fine move involving the pair should have brought a third goal five minutes into the second half.
Suarez smartly clipped a Gerrard pass forward to send Sterling clear again, but this time the 18-year-old could not match the composure he showed for his goal as he fizzed a shot well wide.
Liverpool did add a third two minutes later when Gerrard delivered a pass from 60 yards for Suarez to collect and shoot beyond Mignolet from close range.
From then on, Liverpool were firmly in control and had plenty of chances to add to their advantage.
A Gerrard shot deflected off Glen Johnson towards goal but Mignolet did well to push the ball over the bar, before the Sunderland keeper raced out to deny Suarez his hat-trick.
Both Johnson and substitute Joe Allen had efforts ruled out for offside, but with the damage already done, Liverpool comfortably saw out the remainder of the game to ensure 2013 got off to the ideal start.
Liverpool manager Brendan Rodgers said: "The star was our team. Luis Suarez got two goals and Raheem Sterling got one but that is their job and the team was brilliant.
"It was the fourth game in a short period of time and their work rate and intensity was incredible. I am very, very happy, it is another win for us and we can look forward to the next game.
"Luis has been absolutely fantastic. He moves well, he is a real threat and he is a real pleasure to work with. He is that Lionel Messi type of player in that he gets kicked all over the place but he gets up and he produces."
Sunderland manager Martin O'Neill said: "At half time in the game we felt as if we could have got a goal and we perhaps created the better chances, but we were unable to take them.
"They got the third goal and that was important. If we scored before then it would have got us back into the game but at 3-0, Liverpool are very strong.
"With the Christmas period we have had, if you had said we would get six points from four games against the teams we have played, I probably would have accepted that. It is up to us now, we have some points on board but it is still a tough old time."
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Live Text Commentary
Full Time The referee blows for the end of the match.90:00 +1:59
Short corner worked by Steven Gerrard, Shot on goal by Glen Johnson from long range goes harmlessly over the target.90:00 +1:45
Jesus Fernandez Saez takes a shot. Blocked by Carlos Cuellar.87:22
The assistant referee flags for offside against Luis Suarez. Indirect free kick taken by Simon Mignolet.86:07
Stewart Downing is caught offside. Simon Mignolet restarts play with the free kick.84:19
Joe Allen produces a right-footed shot from deep inside the six-yard box which goes wide of the left-hand post.83:00
Effort from outside the box by Steven Gerrard goes wide right of the target.82:49
Luis Suarez takes a shot. Blocked by Carlos Cuellar.81:34
Inswinging corner taken by Adam Johnson from the right by-line played to the near post, Andre Wisdom makes a clearance.81:08
Luis Suarez gives away a free kick for an unfair challenge on James McClean. David Vaughan takes the free kick.79:39
Glen Johnson has shot on goal from a long way out that goes wide left.79:17
Unfair challenge on Glen Johnson by Fraizer Campbell results in a free kick. Steven Gerrard restarts play with the free kick.77:48
The ball is delivered by Adam Johnson.75:59
Craig Gardner sends in a cross, Jose Reina makes a save.74:38
The referee blows for offside against Luis Suarez. Craig Gardner takes the free kick.73:43
The assistant referee flags for offside against Glen Johnson. Indirect free kick taken by Simon Mignolet.72:32 Substitution
Substitution (Liverpool) makes a substitution, with Jamie Carragher coming on for Martin Skrtel.72:32 Substitution
Substitution David Vaughan comes on in place of Danny Rose.72:22
Jesus Fernandez Saez crosses the ball, James McFadden makes a clearance.71:42
Steven Gerrard takes the outswinging corner, Craig Gardner makes a clearance.
Joe Allen takes a shot. Danny Rose gets a block in.70:35
Luis Suarez is flagged offside by the assistant referee. Indirect free kick taken by Carlos Cuellar.68:42
Luis Suarez takes a shot. Save by Simon Mignolet.67:24
Luis Suarez takes a shot. Save made by Simon Mignolet.66:11 Substitution
Substitution Jordan Henderson leaves the field to be replaced by Jesus Fernandez Saez.66:11
Outswinging corner taken by Stewart Downing, Headed effort from deep inside the penalty area by Daniel Agger misses to the left of the goal.65:51
Glen Johnson takes a shot. Save by Simon Mignolet.65:31
The ball is delivered by Stewart Downing, Steven Gerrard takes a shot.63:27
Stewart Downing is ruled offside. Simon Mignolet restarts play with the free kick.61:17 Substitution
Substitution James McFadden joins the action as a substitute, replacing Sebastian Larsson.60:20
Glen Johnson sends in a cross, save by Simon Mignolet.59:13
Luis Suarez has an effort direct from the free kick.59:13 Booking
Booking The referee shows James McClean a yellow card for unsporting behaviour.59:00
Foul by James McClean on Luis Suarez, free kick awarded.58:42
Outswinging corner taken right-footed by Steven Gerrard from the right by-line, clearance by Fraizer Campbell.58:04
Steven Gerrard takes a shot. Jack Colback gets a block in.57:35
A cross is delivered by Adam Johnson, Jose Reina makes a save.56:58
Inswinging corner taken by Adam Johnson from the right by-line, clearance by Glen Johnson.56:21
Direct free kick taken by Simon Mignolet.56:21 Substitution
Substitution Joe Allen on for Raheem Sterling.56:21
Free kick awarded for an unfair challenge on James McClean by Raheem Sterling.54:54
Jack Colback delivers the ball, save by Jose Reina.53:45
Corner taken by Stewart Downing from the right by-line, Steven Fletcher makes a clearance.53:38
Stewart Downing delivers the ball, clearance made by Danny Rose.51:59
Steven Gerrard provided the assist for the goal.51:59 Goal scored
Goal! - Luis Suarez - Liverpool 3 - 0 Sunderland Luis Suarez fires in a goal from inside the area low into the middle of the goal. Liverpool 3-0 Sunderland.49:45
Raheem Sterling takes a shot.49:01
Glen Johnson sends in a cross, Danny Rose manages to make a clearance.47:56
Foul by Matthew Kilgallon on Luis Suarez, free kick awarded. Steven Gerrard takes the free kick.46:54
Corner taken left-footed by Stewart Downing from the left by-line, Daniel Agger takes a shot.46:45
The ball is swung over by Jordan Henderson, clearance made by Craig Gardner.45:01
The referee starts the second half.45:01 Substitution
Substitution Stephane Sessegnon leaves the field to be replaced by Fraizer Campbell.45:00 +1:09 Half time
Half Time The half-time whistle blows.43:56
Leiva Lucas challenges Sebastian Larsson unfairly and gives away a free kick. The free kick is delivered right-footed by Sebastian Larsson from right channel, save by Jose Reina.41:26
Corner taken by Stewart Downing, Martin Skrtel has a headed effort at goal from deep inside the area missing to the right of the goal.40:13
Raheem Sterling fouled by Jack Colback, the ref awards a free kick. The free kick is swung in right-footed by Steven Gerrard, Craig Gardner manages to make a clearance.37:57
Corner taken short by Luis Suarez.37:42
Stewart Downing takes a shot. Craig Gardner gets a block in.36:16
Luis Suarez takes a shot. Simon Mignolet makes a save.34:42
Inswinging corner taken by Sebastian Larsson from the left by-line, clearance by Daniel Agger.34:20
Matthew Kilgallon takes a shot. Save made by Jose Reina.33:11
Steven Fletcher fouled by Martin Skrtel, the ref awards a free kick. Shot comes in from Sebastian Larsson from the free kick.32:46
Jordan Henderson takes a shot. Comfortable save by Simon Mignolet.32:04
The referee gives a free kick against Raheem Sterling for handball. Simon Mignolet takes the direct free kick.30:08
Sebastian Larsson takes a shot. Save by Jose Reina.29:39
Sebastian Larsson takes a inswinging corner.28:22
Free kick awarded for a foul by Steven Gerrard on Stephane Sessegnon. Direct strike on goal from the free kick comes in from Craig Gardner, Leiva Lucas gets a block in.27:43
Close range shot by Stewart Downing misses to the left of the goal.25:24
Assist by Steven Gerrard.25:24 Goal scored
Goal! - Luis Suarez - Liverpool 2 - 0 Sunderland Luis Suarez fires in a goal from the edge of the penalty box to the bottom left corner of the goal. Liverpool 2-0 Sunderland.24:36
Adam Johnson crosses the ball, Daniel Agger manages to make a clearance.24:02
Free kick awarded for a foul by Martin Skrtel on Steven Fletcher. Stephane Sessegnon takes the direct free kick.23:47
The ball is swung over by Luis Suarez, clearance by Carlos Cuellar.21:21
Shot by James McClean from deep inside the penalty area misses to the right of the target.18:18
The assist for the goal came from Luis Suarez.18:18 Goal scored
Goal! - Raheem Sterling - Liverpool 1 - 0 Sunderland Raheem Sterling finds the back of the net with a goal from inside the area low into the middle of the goal. Liverpool 1-0 Sunderland.17:34
A cross is delivered by Stewart Downing.15:10
Free kick awarded for a foul by Jordan Henderson on Sebastian Larsson. The free kick is delivered right-footed by Sebastian Larsson from left channel, clearance by Glen Johnson.12:23
Jordan Henderson takes a shot. Simon Mignolet makes a save.12:04
Outswinging corner taken right-footed by Steven Gerrard played to the near post, Carlos Cuellar manages to make a clearance.10:56
Unfair challenge on Luis Suarez by Matthew Kilgallon results in a free kick. Stewart Downing produces a shot on goal direct from the free kick, save by Simon Mignolet.9:44
A cross is delivered by Stephane Sessegnon, clearance by Daniel Agger.8:14
Stewart Downing is caught offside. Indirect free kick taken by Simon Mignolet.8:06
Steven Gerrard crosses the ball, clearance made by Carlos Cuellar.7:04
Andre Wisdom takes a shot from inside the box clearing the bar.6:18
Stewart Downing crosses the ball, Matthew Kilgallon makes a clearance.5:44
Handball decision goes against James McClean. Free kick taken by Jose Reina.4:57
Corner taken right-footed by Sebastian Larsson from the left by-line to the near post, Daniel Agger makes a clearance.4:44
Craig Gardner takes a shot. Martin Skrtel gets a block in.4:06
Martin Skrtel gives away a free kick for an unfair challenge on Steven Fletcher. Free kick crossed by Adam Johnson, Daniel Agger manages to make a clearance.0:00
The game kicks-off.
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