Jermaine Beckford continued his superb scoring record in the FA Cup with both goals against a plucky Swindon side.
Beckford, who bagged a hat-trick against Nottingham Forest in the third round, added to his cup tally from close-range in the fifth minute.
League Two Swindon grew into the contest and were thwarted when Sean St Ledger's block denied Matt Ritchie.
But the Championship side doubled their lead when Beckford steered in after Paul Gallagher's run and cross.
Much of the focus before kick-off had been on Swindon's eccentric Italian manager Paolo di Canio, who has guided Swindon into League Two promotion contention while attracting his share of controversy in the process.
Di Canio had said his players deserved a plaque at the County Ground to honour their victory over Wigan there in the previous round, but any hopes he harboured of seeing those heroics repeated here here struck an early blow.
The Robins were behind in the fifth minute, Beckford firing in a half-volley from 12 yards after Foxes captain Matt Mills returned the ball to the penalty when Swindon failed to properly clear a corner.
Swindon took their time to settle but, once they did, looked increasingly impressive, and Foxes goalkeeper Kasper Schmeichel was called upon to make a string of saves in the first half.
It took a superb save by the Dane to keep out Oliver Risser's header from Ritchie's cross.
Schmeichel was called upon again just before the half-hour mark to parry Alessandro Cibocchi's shot from the edge of the box.
And Ritchie thought he had equalised soon afterwards but a last-ditch challenge by Sean St Ledger deflected his six-yard effort over the crossbar.
But Swindon were caught out at the beginning of the second half when Beckford scored with a rising shot from close to the penalty spot after Gallagher's cross from the right.
The goal took Beckford's tally to 14 goals in as many games this season.
The League Two visitors were less of a threat in the second half and Leicester could have made it three but St Ledger and David Nugent spurned chances.
Leicester City boss Nigel Pearson: "Scoring early goals in each half is really important for us. I think they played well in the first half and caused us a few problems.
"I'm pleased with how our players applied themselves. We didn't play as well as we would've liked in the first half but the second half we controlled and once we got the second goal we were very dominant.
"The FA Cup always throws up difficult fixtures and for us, it was always going to be a case of winning the game."
Swindon manager Paolo Di Canio thought Leicester defender Paul Konchesky should have been sent off for a heavy tackle which left Simon Ferry needing lengthy treatment to an injured knee.
"It was clear it was a red card. It was a bad tackle. The referee made a mistake. The foot on the leg was very high.
"We started very shy and then started to play more freely and had chances to draw level.
"The second half was more difficult after their second goal. We lost a bit of belief and energy.
"In general we have to be proud of the players and the fans who really tried to encourage the players."