Pep Guardiola's side suffered its heaviest home Premier League defeat under the Spaniard on Monday (AEST) when Leicester City handed it a humiliating 5-2 defeat.
A brace from Raheem Sterling at Turf Moor ensured City washed away some of the bitter taste from that defeat and Spanish forward Torres, a close-season signing from Valencia, added City's third goal.
City has won this competition four times in the past five seasons and remains on course to retain the trophy.
Guardiola's men would have won by an even bigger scoreline but for a fine display from Burnley keeper Bailey Peacock-Farrell.
Sterling and Kevin De Bruyne both started in a strong City side that also included Riyad Mahrez and a debut for 18-year-old midfielder Cole Palmer.
Sterling made the breakthrough 10 minutes before the interval with a powerful strike from Benjamin Mendy's cross.
The City forward doubled his tally on 49 minutes, finishing off a good move involving De Bruyne and Torres.
City put the result beyond doubt in the 65th minute when Sterling failed to control a Mahrez pass and the ball ran through for the 20-year-old Torres to slam past Peacock-Farrell.