Juan Mata and David Luiz were included from the start by Jose Mourinho, as they look to prove their worth to the Portuguese coach, but it was Torres who stole the show at the County Ground.
The Spanish striker edged Chelsea in front just before the half-hour mark, tapping home after Wes Foderingham could only parry a Mata effort into his path.
Some nimble footwork from Torres and a perfectly-weighted pass slid into the path of Ramires - who replaced the unfortunate Marco van Ginkel after he fell awkwardly and twisted his knee - allowed the Premier League outfit to double their lead 10 minutes before the interval, with a clever dinked finish glancing in off the inside of the post.
League One hopefuls Swindon thought they had found a route back into the game early in the second half, as Dany N'Guessan glanced in a Jay McEveley free-kick, but he and the Robins were denied by an offside flag from the assistant referee.
Mourinho is fully aware of the importance of a much-maligned competition having successfully targeted the League Cup as his maiden piece of silverware during his first stint in charge of the London club, winning it in 2005 and then again in 2007.
And he sent out his clear intentions this time around as he named a strong second string at a sold-out County Ground, worth an estimated £185million compared to Swindon's £550,000.
Most of the pre-match attention was on Mata and Luiz, omitted altogether from Mourinho's matchday 18 for Saturday's 2-0 win at Fulham, with the Blues boss insisting the former has a future at the club but challenging the Spaniard to adapt his game.
And Mata, the club's player of the year for the past two seasons, certainly put in an industrious, roving performance.
His defence-splitting pass sent Torres clear while, just two minutes later, the midfielder looked destined to score himself, only for impressive Town goalkeeper Foderingham to parry his effort into the path of Torres for the opener.
Torres turned provider with a neat bit of skill to set up Ramires soon after and that was the way it stayed - with two clinical attacks proving the difference against a flat-footed Swindon backline.
It was hardly a vintage performance - which could have been more convincing had Torres and Willian made more of second half opportunities - but Chelsea did enough and can now turn their attentions to Saturday's crucial Premier League clash at title rivals Tottenham Hotspur.
Swindon, meanwhile, could be proud of their display and saw a chance of their own chalked off shortly after half-time as N'Guessan was correctly ruled marginally offside with his header.