Leicester went ahead on nine minutes at Holmes Park when George Hirst finished from close range, before Josh Felix-Eppiah made it 2-0.
A brilliant strike from Admiral Muskwe just before the half-hour put the Foxes 3-0 up, but Derby pulled a goal back on 38 minutes through Jahmal Hector-Ingram.
The home side restored their three-goal advantage four minutes before half-time when captain George Thomas found the net.
It is the sixth successive win across all competitions for the Foxes' Under-23 side, who stay fourth in Division 1 on 19 points.
Derby are two places and two points above Leicester and missed the chance to leapfrog leaders Chelsea.
Rayhaan Tulloch put the hosts in front on two minutes before Rumarn Burrell levelled for Boro. Second-half strikes from Chris Willock, Jamie Soule and Dara O'Shea sealed the win.
Tre Pemberton and William Forrester struck either side of Adam Wilson's goal to put Stoke 2-1 ahead, but Elliot Anderson, Tom Allan and Rosaire Longelo gave Newcastle the victory.