First-half strikes from Fernando Torres and Ramires handed the visitors victory against the League One side, as the recently exiled duo returned to Jose Mourinho's teamsheet.
Juan Mata and David Luiz, who had notably been left out of the Blues lineup against Fulham on Saturday, were both involved in a 2-0 win at the County Ground.
Two goals in six first-half minutes from Fernando Torres and Ramires gave the visitors the win, although their success was tempered by the loss of Marco van Ginkel and Ramires to injury.
Torres opened the scoring in the 29th minute with a poacher’s finish after Mata saw his shot saved by Wes Foderingham. Ramires doubled the lead soon after as he lifted a ball into the net following a neat pass from Torres, who had wriggled free outside the area in expert fashion.
As well as the returns of Mata and Luiz, Jose Mourinho gave Mark Schwarzer his Chelsea debut in goal, Cesar Azpilicueta made his 50th club appearance, and Kevin De Bruyne and Willian started as well.
Swindon boss Mark Cooper made one change from the side victorious against Bristol City last time out, with Alex Pritchard replacing Louis Thompson in midfield.
Chelsea was forced into an early change when young Dutchman Van Ginkel twisted his knee after falling awkwardly, with the 20-year-old appearing to be in a lot of pain as he hobbled off in the 10th minute. After the injury and a tight opening to the game, Mourinho’s men had the first sight of goal midway through the half.
Mata threaded a neat ball into Torres's path, and the striker cut in front of his man but saw Foderingham make a save with his head to deny him. Minutes later, though, the former Liverpool man made no mistake as he broke the deadlock after neat build-up play between Ramires and Mata.
Mata’s shot was saved by Foderingham, but Torres was on hand to pounce on the loose ball and poke home from a matter of inches.
Torres then turned provider in the 35th minute as the visitors doubled the lead. The Spaniard played a perfectly weighted pass for Ramires to run onto inside the penalty area, leaving the Brazilian to calmly lift the ball over the advancing keeper and into the back of the net.
Danny N’Guessan thought he had halved the deficit for the hosts early in the second half when he met a Jay McEveley free kick and headed past Schwarzer, but the goal was ruled out for offside. Swindon provided more of an attacking threat after the break, but Schwarzer was rarely tested in the Chelsea goal.
The hosts were nearly punished for pressing forward in the closing minutes but Torres and Willian were both denied by resilient defending as the Premier League side eased through to round four.