All three Swansea goals were of real quality after a flat first period, with young defender Ben Davies scoring his first goal in senior football before Jonathan de Guzman curled home an excellent free-kick.
With nine minutes to go, De Guzman got his second of the game after a delightful Danny Graham flick, and there was time for an injury-time consolation from Michael Owen for Stoke.
Both sides made significant changes from those that faced FA Cup replays in midweek. Garry Monk came back into the Swansea side that made six changes. Ki, Michu and Ashley Williams were recalled, whilst Leon Britton was rested and Chico Flores injured. For Stoke, Kenwyne Jones, who was has been the subject of a rejected bid from Swansea, was dropped in favour of Peter Crouch.
Swansea started brightly, and Pablo Hernandez forced Begovic to tip wide of the post before noticing that he had been flagged offside. A minute later Michu was teed up by Itay Schechter, but could only fire high over the bar on his left foot.
Stoke's best chance came when Matthew Etherington played a one-two with Charlie Adam but slided his shot wide of the post from eight yards with Crouch well placed in the middle.
The hosts then spurned the best chance of the first half when Angel Rangel dispossessed Matthew Etherington near the goal line, and his cross was perfect, finding Michu seven yards out. The Spaniard, looking for his 14th Premier League goal of the season, could only head the ball inexplicably wide.
Swansea took the lead four minutes into the second half when left-back Davies ventured forward, shrugged off Walters and surged into the area before providing an accomplished finish, rolling the ball past Begovic.
Five minutes later, the home side's lead was doubled. Adam bundled over Michu 20 yards out, and De Guzman curled a free-kick home expertly into the top left-hand corner.
With 20 minutes to play, substitute Cameron Jerome somehow managed to miss from three yards, after a cross into the box fell at his feet via the head of Ashley Williams.
Swansea wrapped things up with a wonderful team move ith nine minutes to go. The ball was played into the feet of Graham, and the striker played a delightful one-touch flick round the corner to De Guzman, who finished with ease.
There was still time for Owen to grab a consolation for Stoke with a glancing header in stoppage-time, but there were few cheers from players or supporters following the striker's first goal for the club.