In a thoroughly one-sided local derby, home captain Steven Gerrard set the ball rolling when he headed 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.
Everton also lost Romelu Lukaku to injury in the first half, and they endured more misery after the break when Luis Suarez got in on the act with his 23rd goal of the campaign.
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 their city rivals and never looked like securing their first win at Anfield since 1999 as Liverpool moved four points ahead of them to enhance their chances of securing at 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 line-up, 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 on.
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 were 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 were caught out again almost instantly by Kolo Toure's ball over the top and Sturridge made them 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 they came forward and Suarez put them 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 on, before Sturridge wasted another great chance when he tried to be too clever after Coutinho had played him through on goal.
