Liverpool moved up to eighth in the Premier League table as they comfortably beat Sunderland 3-0 at Anfield.
The Reds scored twice before the break through Raheem Sterling and Luis Suarez with the Uruguayan adding his second after the interval to secure the points for the home side.
With manager Brendan Rodgers back on the bench after illness, this was Liverpool's fifth win in seven Premier League games while Sunderland remain in 14th just four points above the drop zone.
Sunderland had begun the game fairly brightly but it was the home side that forced the first save of the game when Stewart Downing fired in a free-kick that Simon Mignolet had to push wide.
There was nothing the Belgian goalkeeper could do about Sterling's opener inside 20 minutes, although the move did come from his own kick.
The ball came back out to Suarez who chested it down before hooking the ball over his shoulder for the onrushing Sterling to chase and expertly lob over the advancing keeper.
The Black Cats were an intermittent threat at the other end with Steven Fletcher threading James McClean in on goal but the Irish winger missed the target when well placed.
Just minutes later Liverpool were two goals up. Carlos Cuellar fouled Suarez out near the flank but then lost balance and referee Phil Dowd elected to play on as the Uruguayan raced clear to finish.
That proved to be the end of Sunderland's hopes of making a game of it as Suarez had his second of the night shortly after the half-time interval.
Steven Gerrard produced a trademark arrowed pass from deep that exposed the gap in the visitors' defence for Suarez to latch onto the ball and force a shot past Mignolet to seal the victory.
The brilliant forward searched in vain for a hat-trick goal as Liverpool continued to press but it was not forthcoming. No matter, as this was a comprehensive home win to kick-off 2013.
Harry Redknapp's Rangers picked up only their second Premier League victory of the season as they stunned European champions Chelsea at Stamford Bridge.
Former Blues winger Shaun Wright-Phillips scored the only goal with 12 minutes left and although Rangers remain bottom on goal difference, they are now five points from safety.
Luis Suarez struck twice as Liverpool beat Sunderland 3-0 at Anfield.
Raheem Sterling put the hosts ahead after 19 minutes before the Uruguayan striker's brace secured the points to take the Reds up to eighth.
Substitute Victor Anichebe's scored the winner for Everton as Newcastle's poor form continued with a 2-1 defeat at St James' Park.
Papiss Cisse gave the hosts the lead in the second minute before Leighton Baines' thunderbolt free-kick levelled the scores two minutes before the break.
Anichebe, who replaced Steven Naismith in the 58th minute, finished from close range on the hour to send the Toffees fifth.
The 27-year-old Lille full-back travelled to the North-East after the Magpies and Lille agreed a fee, understood to be in the region of ?5m, at the weekend.
However, with a medical to complete and personal terms to discuss, his transfer appears unlikely to be concluded until later in the week.
Debuchy has been in Newcastle's sights for some time, and manager Alan Pardew was hugely disappointed to miss out on one of his major targets after the two clubs were unable to reach agreement over him despite protracted negotiations during the summer.
However, with Danny Simpson having rejected the Magpies' latest contract offer with his current arrangement due to expire at the end of the campaign, the right-back position has become a priority.
Ba's exit from St James' Park moved a step closer on Wednesday when the Blues finally triggered the release clause in his Magpies contract.
The Blues have been given permission to talk to the 27-year-old Senegal international after meeting the ?7million figure stipulated in the deal he signed with the Magpies during the summer of 2011.
Ba was withdrawn from the Newcastle squad for Wednesday's Premier League clash with Everton at St James' Park as a result.
Although a deal for Ba has not been finalised, Pardew - speaking before the Everton game - told Sky Sports 1: "It's done. He will go to Chelsea with our blessing. He has done fantastic for us and it's not a bad thing, all the uncertainty is now done and we can move on.
"This club is bigger than any player for sure."
