A goal in each half from striker Jermaine Beckford ended Town's impressive FA Cup run at The King Power Stadium, but it was a spirited performance from the Robins.
Town manager Paolo Di Canio made one enforced change to the side with Aden Flint missing the game through injury and he was replaced by Alan McCormack following the completion of his two-game ban.
The home side went on the attack from the off and took just four minutes to break the deadlock. After a corner had been half-cleared, the ball was cut back by Matt Mills with Jermaine Beckford on hand to sweep the ball home from the edge of the six-yard box.
Town composed themselves after the goal but it was the home side who continued to pile forward early on. Wes Foderingham made a good stop from Beckford but play was soon brought to an end for a foul.
With a quarter of an hour played, Town took the game to the hosts with a spell of possession which first saw Alessandro Cibocchi's free-kick blocked before Simon Ferry fired over with a left footed effort from the edge of the box on 19 minutes. Another chance fell Swindon's way on 22 minutes with a free-kick in from the right by Matt Ritchie was met by Alan Connell who brought a smart save out of Kasper Schmeichel.
Good play from Raffaele De Vita and Ferry saw the two combine well before the Italian saw his shot squirm through to be claimed by the Foxes stopper. Just after the half-hour a left foot shot from Connell was palmed onto the bar by Schmeichel with Town pressing. On 39 minutes, with the Robins playing excellent football, it could have been one all. An initial shot from Connell from a Cibocchi cross was blocked before Ritchie's follow up deflected over.
Chances continued to fall for the Robins before the break with Ferry and Risser having a go but the home side stood firm. The Foxes could have been down to ten men in first half injury time, but Paul Konchesky's late challenge on Ferry earned just a caution. Both sides emerged unchanged for the second half, with the Foxes wasting little time in doubling their advantage. After a barnstorming finish to the first half from Swindon, it was the home side go got the all-important second goal of the game. A cut-back from the right by David Nugent was eventually hammered home by Beckford from close range to double the home advantage.
Di Canio responded by throwing on Lander Gabilondo in place of De Vita on 54 minutes before a second change which saw Ronan Murray on in place of Connell. Swindon continued to venture forward with chances falling their way without really testing Schmeichel. Wes Foderingham produced a superb stop to deny a Leicester third on 75 minutes, diving low to his left to palm away a header from Nugent.
Louis Thompson replaced Ferry for the final ten minutes of the game with the youngster given a chance to impress on the big stage in front of more than 19.000 fans.
Town did have second half opportunities but the Foxes controlled the game in the latter stages to safeguard their place in Sunday's FA Cup with Budweiser fifth round draw. Swindon's excellent away support continued in full voice right the way through the encounter, with all eyes now turning to Tuesday's League 2 encounter at Southend United.