Leicester had never beaten Chelsea in six previous meetings in the competition, and first-half goals from Gary Cahill – who sent out an emotional message to his stricken former team-mate Fabrice Muamba in his celebration - and Salomon Kalou meant that the Foxes never looked like ending that run.
Torres then capped an excellent all-round performance midway through the second half with his first goals in more than 25 hours of playing time in a Chelsea shirt.
Jermaine Beckford scored a consolation for Leicester, but Torres restored the three-goal advantage by heading home his second of the game five minutes from time. Substitute Ben Marshall then scored the best goal of the match in the closing moments, only for Torres to set up Raul Meireles in injury time to take his tally for the match to two goals and two assists.
Chelsea's interim manager Roberto Di Matteo made a raft of changes from the side which beat Napoli in midweek. Captain John Terry was missing through injury, while Fernando Torres started up front and Ryan Bertrand and Kalou made rare starts for the Blues.
For Leicester, Paul Konchesky's return from suspension was the only change for Nigel Pearson's team which beat Birmingham City on Tuesday.
Leicester showed plenty of attacking intent early on, but it was Chelsea creating all the chances and they went ahead after 12 minutes.
Goalkeeper Kasper Schmeichel stayed on his line as Juan Mata swung a corner into the six-yard box, and Cahill leapt ahead of Wes Morgan to head home his first Chelsea goal on his ninth appearance for the club. The former Bolton defender lifted his shirt to reveal a t-shirt bearing the message "Pray 4 Muamba", a touching tribute to his former Trotters team-mate who remains in a critical condition after suffering a cardiac arrest at Tottenham on Saturday.
A bright looking Torres had won the corner which led to the opening goal, and he had an even bigger hand in the second. His surging run down the right enabled him to play the ball square for Kalou, who snuck the ball under the advancing Schmeichel for his fourth of the season.
Chelsea had several chances to add to that lead soon afterwards, with Sturridge lifting the ball over the keeper but wide of the far post before Torres twice drew saves from Schmeichel after being set up by Mata.
Beckford drilled a tame effort wide before Neil Danns's solid strike drew forced a diving save from Petr Cech, but that was the only time the Czech keeper's goal was truly threatened in the first half.
Di Matteo's team selection certainly seemed to have Wednesday's vital Premier League clash with Manchester City in mind, and at half-time he gave Mata a rest by replacing him with Florent Malouda. The Frenchman had two chances within 10 minutes of coming off the bench – firstly forcing a save from Schmeichel before firing another effort wide of the near post – but it would be Torres who would score next, ending his barren run in the process.
On 67 minutes Meireles was played down the left by Sturridge and the Portuguese picked out Torres in the box. The Spaniard took two quick touches with his right foot – the first to control and the second to sidefoot past Schmeichel – for his first goal since his brace against Genk in the Champions League last October.
Beckford went alone at the top of the scoring charts in this season's competition when Neil Danns's 77th-minute effort rebounded off the post and the former Leeds striker fired past Cech.
Having waited five months for a goal, Torres only had to wait another 18 minutes for another when he glanced a near-post header into the far corner from Meireles's corner.
Marshall then curled an outstanding strike into the top corner from 25 yards that Cech could only watch helplessly sail past him on 89 minutes, but Torres had the last word in stoppage time when he powered down the left and into the box, leaving Sol Bamba flat on his front, and squared for Meireles to fire past Schmeichel.