Torres joined Chelsea from Liverpool for 50 million pounds in January's transfer window but has struggled to find the form that made him one of the most feared strikers in the game last season and had gone 13 games without a goal.
Manager Carlo Ancelotti has recently been starting with Torres among the substitutes and he came on again for the last 14 minutes at Stamford Bridge on Saturday.
With six minutes remaining he ran on to a Nicolas Anelka through pass and, after initially appearing to lose control of the ball as it got stuck on a pitch made sodden by heavy rain, he turned sharply and swept the ball home.
The striker was immediately engulfed by all his team mates while Ancelotti pumped his fists in a joyful celebration.
Torres completed a highly satisfactory evening's work by setting-up Florent Malouda for Chelsea's stoppage-time third goal in a win that kept them six points behind leaders Manchester United with four games to go.
"I have had 14 games (including Saturday's) waiting for a goal, which was not the beginning I was expecting when I signed for a massive team like this," Torres told the BBC.
"It is not easy when you sign for a club in January but I want to thank all my team mates because they have been looking out for me all this time. There will be less pressure on me now. Now we can try and finish the season as we all want.
The Spaniard added: "It has not been difficult (not scoring) because the fans have been very patient with me showing their support every game. I wanted to show them I could score and hopefully this is the first of many."
Didier Drogba, who made way for Torres having performed impressively up front, told ESPN: "We know we have a great player here. Next season is going to be fantastic for him.
"The most important thing today is the three points and Nando's goal. We have to focus on second place. Winning this game and being in front of Arsenal is the first step."
Ancelotti said it had been a perfect day.
"Everyone expected Fernando to score and finally he scored and for him from today will be a new life," he said.
"He needed to score this goal. He worked hard and maintained confidence and composure and from today he will have a fantastic future at this club.
"The big problem was that he came into a new club and it was not easy to immediately find a good understanding with his team mates and he had these difficulties but now the bad moment is gone and we will take advantage with his performances."
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