The Uruguayan forward was in superb form, grabbing two goals and setting up the other for Raheem Sterling, with Martin O'Neill's side guilty of some sloppy defending throughout
The hosts raced into the lead through Raheem Sterling, who produced a fantastic lob to beat Simon Mignolet in the Sunderland goal after racing through to Luis Suarez's fantastic pass.
The Uruguayan forward doubled his side's advantage before the half hour mark after bursting past a cynical challenge from Carlos Cuellar near the touchline, with referee Phil Dowd waving play on, before finishing with aplomb with the outside of his right boot past the goalkeeper.
Some exceptionally poor defending allowed Suarez to find himself in acres of space after latching on to Steven Gerrard's brilliant long pass into feet before calmly slotting home to make it three.
Liverpool manager Brendan Rodgers made two changes to the side that beat QPR last time out, with Andre Wisdom and Lucas coming in for Jose Enrique and Joe Allen.
Sunderland boss Martin O'Neill meanwhile made just the one change to the team that lost to Tottenham at home at the weekend, with the injured John O'Shea replaced by Danny Rose.
After a bright opening from the hosts, Stewart Downing forced Mignolet into a fine save at his near post as he tipped the winger's free kick from a promising position outside the area behind for a corner.
They didn't have to wait much longer to take the lead in the 18th minute through Sterling, though, after he latched on to Suarez's looped pass over the back four and coolly lobbed the ball over the onrushing Mignolet.
The visitors should have grabbed an equalizer shortly afterwards following a flowing move involving Steven Fletcher, Stephane Sessegnon which resulted in James McClean screwing his effort well wide with the goal gaping.
They were made to pay for this profligacy in front of goal in the 26th minute when Suarez doubled Liverpool's tally after out-muscling Cuellar wide on the right before driving into the box and slotting home through Mignolet's legs.
With the game becoming increasingly open, Matt Kilgallon wasted an excellent chance at the back post after a superb ball to the back post from Adam Johnson, with Pepe Reina saving well with Steven Fletcher lurking before Downing went close after another breakaway move after a great piece of improvisation from Henderson.
After the break, Suarez once again played Sterling through with a sublime pass around the corner, but Mignolet pulled off a smart stop down low to his right to push the ball away.
With the visitors struggling to get any sort of tempo going, though, after a sustained period of possession, Suarez bagged his second of the game in the 52nd minute after collecting Gerrard's fabulous 50-yard pass before burying the ball into the bottom corner.
It took a flying save from Mignolet to tip Gerrard's deflected volley over the bar, before saving well with his legs to deny Suarez his hat trick moments later.
Glen Johnson and Joe Allen then both saw goals correctly disallowed for offside as the game entered its dying stages and despite carving the visitors open seemingly at will, Liverpool couldn't add to its tally any further, going on to claim all three points with a marvelous team display.