Torres had scored just twice this season before Chelsea's visit to Anfield, fuelling talk that his lacklustre displays were a sign he is keen to leave the Reds.
But the Spanish striker was back to his predatory best as he netted with a cool finish from Dirk Kuyt's pass in the 11th minute and then curled a brilliant second past Petr Cech from the edge of the penalty area just before half-time.
Those two lethal finishes condemned Chelsea to their second league defeat this season and left Carlo Ancelotti's league leaders just two points ahead of second placed Manchester United.
Liverpool's victory extended their recent revival to four successive wins in all competitions and lifted Roy Hodgson's team into mid-table.