The Spain striker had failed to score for Chelsea since October until he found the net in the 67th minute, and he added another goal in the 85th with a near-post header at Stamford Bridge.
"I needed those goals. I've been working so hard to get them," said Torres, who hadn't scored for 25 hours, 41 minutes. "Maybe the job of a striker is to score goals and if you don't do it people think you're playing badly.
"But the support has been here and I feel the confidence of the manager (Roberto di Matteo) now. We have some important games coming."
Gary Cahill opened the scoring with a 12th-minute header. The January signing marked his first Chelsea goal by unveiling a "Pray 4 Muamba" T-shirt in tribute to his former Bolton teammate, who is in intense care after going into cardiac arrest and collapsing in Saturday's abandoned match at Tottenham.
Salomon Kalou doubled Chelsea's lead in the 17th with a neat finish, and Raul Meireles rounded off the win in the 90th.
Jermaine Beckford and Ben Marshall grabbed the consolation goals for second-tier club Leicester.
The win extended Di Matteo's winning run to four matches since replacing Andre Villas-Boas to become interim manager two weeks ago.
"Every win gives the players confidence — you can see they have more confidence," Di Matteo said. "I thought Fernando had a terrific game, he fought very hard for the team and managed to score a couple of goals too. It's wonderful for him.
"I have a lot of belief in him and the other players. He works so hard, and in life if you do that you will get rewarded for it."
Cahill's opener came after rising at the far post to head home Juan Mata's corner.
Torres was involved when Chelsea doubled its advantage five minutes later. He broke into the Leicester half and outpaced Paul Konchesky before sliding the ball through to Kalou, who finished calmly past goalkeeper Kasper Schmeichel.
Moments later, Torres should have ended his goal drought when receiving the ball in the center of box by Mata, but he headed straight at Schmeichel.
The visitors struggled to keep possession for any meaningful length of time but Chelsea sat back.
Torres had another chance just before the hour mark but his left-footed effort was deflected clear, as the Chelsea supporters willed their 50 million-pound striker ($80 million in January 2011) to find a goal.
And the burden was finally lifted from Torres' shoulders when he squeezed Meireles' pass into the corner.
That goal seemed to killed off the game as a contest, but Beckford managed to force Chelsea goalkeeper Petr Cech into a good save with 15 minutes remaining.
But Beckford did manage to score after Neil Danns' effort had crashed against the post.
The three-goal margin was soon restored through Torres' near-post header from Meireles' corner.
But Leicester substitute Ben Marshall scored the goal of the game in bending a shot around Cech and into the corner of the net.