The young Foxes made it three straight victories across all competitions either side of the New Year, with the Toffees dispatched courtesy of two first-half goals from Darren Motsi and Kirsten Otchere.
Fifteen-year-old Motsi opened the scoring 25 minutes in at Walton Hall Park, capitalising when the hosts failed to clear their lines after George Pickford saved Otchere's effort. Motsi picked up the ball, shifting it onto his left before whipping a tidy finish into the opposite corner.
And just over five minutes later it was Otchere's turn to find the net and secure the three points. Luca Davis' throw-in back to Pickford was pounced on by the forward, who nipped in, and despite the defender's the best efforts, it crossed the line.
The result moves City up to sixth in the PL2 standings, having collecting 17 points from 10 matches so far this term. It's a trip to West Bromwich Albion up next on Monday 19 January (7pm GMT kick-off).
The details
City: French, Donnelly, Gray, Amartey (c), Khela; Briggs, Golding (Toko 86'); Richards, Motsi (Neale 77'), Carr (Omobolaji 69'); Otchere (Popov 86').
Unused sub: Donohue.
Goals: Motsi 25', Otchere 31'.