Sidnei Tavares, Dempsey Arlott-John and Terell Pennant struck for the young Foxes at the University of Bolton Stadium to continue their intrepid run in the competition.
After a productive opening 32 minutes, Leicester's youngsters took a deserved lead after dominating the early proceedings at the home of the Sky Bet Championship club.
An ambitious effort from Tavares, around 25 yards out, deflected off a Wanderers defender and wrong-footed goalkeeper Callum James in the home side's net.
Two minutes later, they almost doubled their lead when Pennant's effort was blocked and fell to Tavares, but defender Adam Senior was able to block it.
With 14 minutes remaining in the second half, Arlott-John, a substitute for City, made it 2-0 by finding the bottom corner from 20 yards out.
In the latter moments, meanwhile, the young Foxes added a touch of gloss to the scoreline as Pennant wrote his name onto the scoresheet in added time.
As a result, the Club's youngsters go into the last-eight draw, expected to take place later this week.
City: Bosworth, D. Gyamfi, Thomas, Elewa-Ikpaku, Kranthove, Husek, Pennant, Ewing (James 90'), Russ (J. Gyamfi 90+4'), Tavares, Flynn (Arlott-John 61')
Subs not used: Stolarczyk, Fitzhugh
Goals: Tavares 32', Artlott-John 76', Pennant 90+4'
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