Goals from Callum Wright and Jake Wakeling were not enough for the Foxes to take anything from the Premier League 2 Division 1 encounter in Seagrave.
Two changes were made to the side that beat Manchester United Under-23s last week, with Darnell Johnson - now on loan at AFC Wimbledon - and Ali Reghba making way for Ben Nelson and the returning Sidnei Tavares.
Everton's full-backs combined in the opening stages as Kyle John's cross eventually found Thierry Small and he sent in a shot that was heading on target until Darragh O'Connor deflected it wide.
Leicester also looked for that early goal and almost found it when Khanya Leshabela had a shot cleared off the line, with Vontae Daley-Campbell's follow up blocked. Leshabela was involved again when he carried the ball down the right and fed Wright, but he dragged a shot wide of the target.
Everton were still a threat in attacking areas, however, primarily through Nathan Broadhead, and the forward dug out a powerful shot that goalkeeper Jakub Stolarczyk was equal to.
The visitors soon found themselves ahead with Broadhead the provider, finding Small, who took the ball in his stride and fired past Stolarczyk. The shot-stopper could do nothing to stop the thunderous strike, which came just before the half-hour mark.
City responded well and were back level on 35 minutes via a well worked goal involving a lofted through ball from Leshabela, an excellent first touch from Wakeling to bring the ball under control and a neat first-time finish from Wright.
Parity lasted barely a minute as Everton re-established their lead. Broadhead again was the instigator, supplying the dangerous Iner Iversen, who made no mistake, slotting the ball into the far corner.
Everton's No.9 had the ball in the net himself, latching onto Hughes' through ball, but the offside flag was up. Once again looking to draw level for the Foxes, meanwhile, Tavares had time and space to shoot from range but saw his strike fly over the bar.
And it would be the away side who found the net again as Con Ouzounidis headed in Everton's third from an in-swinging free-kick.
Having lost O'Connor to injury, fellow centre-back Nelson also went off at half-time, leading to re-shuffle at the back for the hosts. Chances were initially few and far between in the second period, as City, despite being on top in terms of possession, struggled to gain any momentum or rhythm going forward, thwarted by an organised Everton back four.
The best early opportunity came directly from a set piece as Tavares went for goal from a free-kick 25 yards out, which was saved by Everton 'keeper Joao Virgínia, low down to his right.
Tavares was soon replaced by Kasey McAteer, whose first involvement was to force another smart stop out of Virgínia, with Wright heading narrowly wide from the resulting corner.
It continued to be all City as Wright opted to shoot from distance and fired into the arms of the Virgínia. Finally, the goal that City's pressure deserved came from Wakeling, who backed up his effort last week with a fine left-footed finish on the turn after Wright's shot had deflected into his path.
A flurry of chances followed, starting with Wakeling's header, from a Leshebela cross, which was held, before half-time substitute Reghba's header, from Callum Hulme's centre, didn't have enough power to beat the 'keeper either.
Shane Flynn got in behind the back four and saw his effort parried away, while Wright couldn't quite get to turn home the follow-up. Leshabela then took the ball down on his chest and ambitiously fired narrowly wide from outside the area, but for all the pressure, the Toffees struck again.
Broadhead found himself through on goal and slotted the ball beyond Stolarcyzk, who made an untimely slip just before the Everton forward found the net.
The Foxes kept battling and Reghba looked to fashion an opening, turning Ouzounidis before striking just past the far post. Wakeling's had another header saved, this time denied by a brilliant diving stop from Virgínia, with McAteer and Leshabela also having efforts saved soon after.
A series of corners came in the closing stages, including when Harvey Godsmark-Ford bundled the ball into the net, only for the referee to rule it out for a foul on the 'keeper and ensuring it was Everton who took home the points.
Major moment…
City went close on numerous occasions to equalising in the second half and having worked so hard to get back into the contest at 3-2, the fourth goal, scored by Nathan Broadhead, ended any real hope of taking something from the game.
The home side were once again trailing by two goals and this time it proved too big a task to come back in the final 10 minutes.
Who impressed?
Speaking during LCFC TV's live coverage, Matt Elliott said: "For me, someone who deserves a lot of credit for his involvement in both Leicester goals is Jake Wakeling. He's created one, scored one and he's had a tough task on his own, initially in the first half. But then in the second half he's been joined by [Ali] Reghba and he hasn't stopped working. He's grafted away tirelessly and he demands the ball, he wants it all the time and Wakeling has put in a great shift this evening."
Where does it leave us?
The Foxes slip down to 11th in the Premier League 2 Division 1 standings, with 15 points collected from 13 games.
Coming up…
Blackburn Rovers Under-23s are the next visitors to LCFC Training Ground for matchday 14, facing City's Development Squad on Monday 1 February (7pm GMT kick-off).
The details…
City: Stolarczyk; Daley-Campbell, O'Connor (Godsmark-Ford 39'), Nelson (Reghba 46'), Flynn; Hulme, Leshabela; Suengchitthawon; Tavares (McAteer 60'), Wakeling, Wright (c).
Subs not used: Doherty, Braybrooke.
Goals: Wright 35', Wakeling 69'.