A superb finish three minutes from time from Chris Wood sealed the victory for Steve Beaglehole’s side, despite the visitors hitting the bar late on through Matthew Kennedy.
First-teamers Liam Moore and Wood gained some valuable game time in a side captained by James Pearson, who recently returned from his loan spell at Wrexham.
Having conceded a late goal in the 1-0 league loss to West Ham last week, City were looking for their first win of 2015, and knew three points could take them as high as ninth.
The Foxes battled through wet and windy conditions, mustering up the first chance with five minutes gone. Elliott Moore’s clearance fell straight to Wood, who turned and hit a half-volley straight at goalkeeper Mateusz Hewelt.
City rode their luck just after the quarter-hour mark when Callum Connolly fired his 16-yard effort over the bar as David Unsworth’s side threatened.
Liam Moore then met Jak McCourt’s corner with a fierce header that flew just over the Everton woodwork – a golden chance to open the scoring.
City Goalkeeper Jonny Maddison had to turn Chris Long’s cross away from goal just moments later before Elliott Moore nodded over at the other end.
Goalless at the break, a fine one-two between Harry Panayiotou and Joe Dodoo saw the latter’s low drive blocked as City applied the pressure.
Young defender Ben Chilwell, who excelled at left-back all game, cleared captain Jonjoe Kenny’s effort off the line while Conor Grant’s strike flew inches wide of Maddison’s right-hand post.
Everton’s carved out their best opportunity on 76 minutes. Kennedy’s 20-yard free-kick curled over the Leicester wall and hammered the bar, but Leicester cleared their lines and survived the scare.
The decisive moment came with 87 minutes gone. Wood pounced on Grant’s loose back-pass and lifted the ball over Hewelt in expert fashion to seal the win for the Foxes.
Securing a first victory since beating Benfica in late November, the Foxes travel to Tottenham Hotspur on Monday 26 January in search of their second successive league triumph.
CITY: Maddison, Pearson (c), Chilwell, Sesay, E. Moore, L. Moore, Stankevicius (Barrington 61), McCourt, Wood, Panayiotou, Dodoo
SUBS NOT USED: Davis, Smith-Varnham, Fox, Rowe
GOAL: Wood 87
EVERTON: Hewelt, Jones, Connolly, Ledson, Browning, Kenny (c), Williams (Dowell 72), Grant, Duffus, Long (Kennedy 62), Henen
SUBS NOT USED: Hunt, Junior, Langton
REFEREE: Simon Barrow