January has been over-hyped as the answer to Liverpool's prayers by their intense longing for the transfer window to reopen. It is far from that, as Brendan Rodgers has been at pains to stress, but it is off to an emphatic start after the swift £12m signing of Daniel Sturridge was accompanied by an eye-catching defeat of Sunderland.

As has been the case since a turbulent summer window increased the responsibility on him, Luis Suárez inspired the Liverpool cause and Martin O'Neill's team could find no response. The Uruguay international, aided and abetted throughout by Steven Gerrard, created the opener for Raheem Sterling and struck twice to take his Premier League total for the season to 15. His latest fruitful display came on the night Jamie Carragher made his 493rd league outing for Liverpool to move ahead of Billy Liddell into outright second on the club's all-time league appearance list, behind Ian Callaghan on 640.

Sturridge watched from the directors' box at Anfield having completed his move from Chelsea earlier in the day and should have been salivating at the prospect of working alongside Suárez. The England international is better late than never as far as Rodgers is concerned but the prospect of finally easing the burden on Liverpool's leading goalscorer might have to wait.

The Liverpool manager drooled: "I spoke to Harry Redknapp about Luis after our game at QPR the other day and we said Luis was a Messi-type character. When I gave him a break at the start of the season he didn't want it. He is a player that has to play two or three times a week to be on top of his game – one game a week is no good to him. He is a real team player and trains every day. He is never in the treatment room and then he comes out and performs like that. His cleverness and intelligence finds the space and he is thriving. It will be fantastic to see him develop because there is still a long way to go for him."

Suárez set the tone against a Sunderland side that carried a threat throughout the first half – and this was not the stroll that Liverpool's previous home win over Fulham represented – before running out of ideas and energy against the Uruguayan's relentless movement, strength and penetration. The Liverpool striker's first telling intervention was to send Sterling clear of the dozing defenders Danny Rose and Matthew Kilgallon with an overhead kick, after Gerrard had headed back a goal-kick from Sunderland's goalkeeper Simon Mignolet. Sterling had time to steady himself before beating Mignolet with a delicate lob.

Anfield celebrations should have been cut short when Stéphane Sessègnon and Steven Fletcher combined to release James McClean inside the Liverpool area. McClean dragged his shot well wide of Pepe Reina's post and had further cause to rue the miss when Suárez doubled Liverpool's lead moments later.

Again Gerrard was involved, winning a challenge and releasing play down the right, and again the Sunderland defence was found wanting as Carlos Cuellar failed to dislodge Suárez with a shoulder charge or clear when the ball fell briefly at his feet. The referee, Phil Dowd, ignored his assistant's flag and played a fine advantage as Suárez advanced into the area and swept the ball beyond Mignolet with the outside of his right foot.

O'Neill's team should have reduced the deficit before the interval but Sebastian Larsson shot tamely at Reina after a Craig Gardner effort deflected into his path. The Liverpool goalkeeper also made an outstanding save low to his left to prevent Kilgallon converting a floated cross to the far post from Adam Johnson. "We needed to take our chances and didn't do that tonight," said the Sunderland manager. "The third goal put us on the back foot and after that Liverpool were really comfortable."

Sunderland had not won at Anfield since October 1983 and, with Jordan Henderson impressing against his former club, Gerrard picking off passes unchallenged and Suárez dominant, not to mention the visitors' own profligacy, there was no prospect of the drought ending here. The second half was more one-sided than the first and Sterling could have added a third when Gerrard and Suárez again combined to send him through on Mignolet's goal. This time the 18-year-old clipped his finish wide of the far post.

The telepathy between Liverpool's captain and leading goalscorer soon inflicted further punishment on the men from Wearside, however. The source was Gerrard, who delivered a stunning pass through the centre of Sunderland's central defence from deep inside the Liverpool half, and Suárez duly applied the necessary finish from close range. It was his fifth goal in five games against Sunderland. Close but correct offside calls prevented Glen Johnson and Joe Allen from adding a fourth for Liverpool.