Around 4,000 Swindon fans made the trip to the East Midlands, making this the largest away following Leicester had had this season so far.
Leicester took an early lead on 5 minutes when Beckford was able to score from close range to make it 1-0.
As the first half progressed Swindon looked better with both Connell and Richie coming close for Swindon.
Leicester could have been reduced to ten men with a two footed foul by Konchesky on Ferry, but only a yellow card was shown.
Leicester started to have more of the play in the second half, and doubled their lead with another goal from Beckford.
Foderingham had to make a good save to prevent Leicester getting a third, but overall it was still a good display for Swindon.