They had further opportunities of putting the game beyond the Foxes, but poor finishing left the result in doubt until the final whistle.
The visitors won the first corner in the eighth minute, but the early play was confined to a packed midfield, although Matty Fryatt did squander a goalscoring opportunity when he spooned over from close range after meeting a Paul Gallagher cross.
Nathan Dyer had the beating of Michael Morrison down the left flank and the Leicester man was booked for bringing the speedy winger down just two minutes after being nutmegged by the Swan.
With 30 minutes gone it was the Swans on top, but despite having more of the play they were unable to prise out any clear openings.
That changed two minutes later when Darren Pratley sent Dyer racing down the right and his cross was deftly turned in by Pintado for his first goal of the season.
Five minutes before the break, the busy Pratley lashed a shot just wide of the far post with Foxes keeper Chris Weale beaten.
No changes were made at the interval and the Swans were quickly back in the groove penning Leicester in their own half.
Pintado should have doubled the score in the 57th minute, but he completely miskicked when in front of goal following a run and cross by David Cotterill.
Steve Howard and Martyn Waghorn joined the fray on the hour as the visitors looked for an equaliser and Waghorn weaved his way into the penalty area, only to delay his shot and the chance was lost.
It was now Leicester's turn to make some headway and Lloyd Dyer sent a ground shot skimming past the post in the 63rd minute, but the Foxes were limited to breakaways and the Swans were soon back on top.
The visitors pushed hard in the closing stages, but the Swans held out for a well-deserved victory.