Substitute Lionel Messi's winner saw Barcelona record a 2-1 victory over Atletico Madrid in Saturday's La Liga encounter at the Vicente Calderon.
Both sides had won their opening two fixtures, but only Barca were able to keep up their perfect record in the Spanish capital.
Atletico got an early chance to open the scoring after Juanfran set up Torres, but the former Liverpool star sliced his volley over the crossbar.
The visitors began to grow into the contest and Ivan Rakitic threatened with 15 minutes gone. Andres Iniesta reached the Croatia international after evading several challenges, but Jan Oblak made a good save to deny the midfielder.
Torres then blasted off target following some excellent work from Antoine Griezmann.
Luis Enrique's men nearly broke the deadlock in the 25th minute via Luis Suarez, only for Oblak to deflect the Uruguay international's shot from close range onto the crossbar with a miraculous reflex.
The Catalans once more came close to the opener 10 minutes before the half-time, as Jeremy Mathieu reached Suarez with a long ball and he in turn found Neymar, only for the Brazilian attacker's attempt to be blocked.
Atletico made a superb start to the second half and felt aggrieved not to be awarded a penalty after Javier Mascherano seemingly handled Torres' cross. They had reason to celebrate shortly after, though, as Tiago opened up the Barcelona defence with a sublime pass and Torres coolly slotted home to make it 1-0.
Martinez was introduced from the bench and had a decent chance to make it 2-2 just five minutes before the final whistle, but the Colombian striker's volley ended in Ter Stegen's hands as the visitors emerged victorious.
