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.