Steven Gerrard opened the scoring before two goals from the England striker put the result beyond doubt before halftime as the visitors slip four points off fourth place.
In a thoroughly one-sided local derby, home captain Steven Gerrard set the ball rolling when he headed in his sixth goal of the season before in-form Sturridge struck twice in as many first half minutes to take his tally to six goals in his last five games and 16 for the season.
|VIEW FROM ANFIELD
|By Gary Maiden
A Daniel Sturridge double and goals from Steven Gerrard and Luis Suarez put Everton to the sword in a surprisingly comfortable victory for Liverpool at Anfield.
Brendan Rodgers’ forward line had too much class for a makeshift Everton defense and, in reality, it could have been more as the visitors simply failed to cope.
The win puts Liverpool in a commanding position in the race for Champions League football, with Tottenham hosting free scoring Manchester City on Wednesday evening.
It will take the Everton faithful a long time to forget this result, but Roberto Martinez must find a way to regain some confidence into his wounded squad as it tries to claw back the four-point deficit on its city rivals.
However, it was Sturridge who stole the show - with the England forward spurning a golden opportunity for his hat trick in the second half as he blazed a penalty into the Kop.
Everton had no answer to its city rivals and never looked like securing its first win at Anfield since 1999 as Liverpool moved four points ahead of the visitors to enhance its chances of securing a top-four finish in the Premier League.
The return of Everton trio Ross Barkley, Steven Pienaar and Antolin Alcaraz softened the blow of losing Bryan Oviedo (double leg fracture) for the visitors, while Phil Jagielka was also passed fit after picking up a knock at Stevenage on Saturday.
Jon Flanagan was preferred to Martin Kelly in the Liverpool starting lineup, with Simon Mignolet and Raheem Sterling also returning.
Barkley looked like he had never been away when he rounded off a swift break with a venomous left-footed strike from outside the penalty area that flashed just over the crossbar early.
Liverpool soon got the upper hand, though, as Tim Howard denied Suarez and Jordan Henderson before Sterling raced onto Sturridge's incisive throughball but failed to beat the United States goalkeeper 17 minutes in.
It came as no surprise when Gerrard rose highest to head in Suarez's corner four minutes later to give Liverpool a deserved lead, and to make matters worse for the visitors, Lukaku suffered an injury which ended his participation in the game.
Everton was then stunned by two goals in as many minutes from Sturridge, as first the England striker raced onto Philippe Coutinho's fine pass and finished clinically with his left foot in the 34th minute.
Roberto Martinez's side was caught out again almost instantly by Kolo Toure's ball over the top and Sturridge made it pay by beating Howard with a sublime lob.
Leon Osman replaced Pienaar at the break and took just three minutes to make an impact as he forced Mignolet into a reflex save.
Liverpool looked dangerous every time it came forward, and Suarez put it out of sight after 50 minutes when he raced clear and calmly placed the ball beyond Howard.
Sturridge had a golden opportunity to complete his hat trick three minutes later, but he put a penalty into the Kop after Howard had upended Sterling in the area.
Everton showed some spirit and Barkley forced a save out of Mignolet late before Sturridge wasted another great chance when he tried to be too clever after Coutinho had played him through on goal.