The Academy outfit came from a goal down on Merseyside, where Cole Palmer converted a penalty to cancel out Lewis Dobbin’s early opener for the visitors.
Gareth Taylor’s side enjoyed spells of dominance and created more chances, but a lack of a cutting edge combined with the host’s stubborn defending meant we had to settle for a point.
In a physical encounter City took time to find our rhythm, falling behind inside 10 minutes after CJ Egan-Riley’s hesitation when trying to play out from the back was punished.
Moments earlier the centre-half had made a saving block to deny Tom Cannon and the forward responded in kind for the opener, denying the defender’s pass before racing clear and squaring for Dobbin to fire past Slicker.
It did nothing to dent Taylor’s side’s confidence and Oscar Bobb forced a good save from Zak-Luk Leban in the Everton goal as our youngsters' passes started to connect.
And it almost yielded the most spectacular of equalisers after an inspired moment of magic from Alex Robertson.
The midfielder showed incredible speed of thought when Palmer’s free-kick was headed clear, arcing his body to execute an overhead kick which cannoned back off the crossbar.
It was a warning and four minutes later City were level.
Overzealous defending from two Toffees’ defenders sent Palmer to the floor in the area and the captain dusted himself down to send the ‘keeper the wrong way from 12-yards.
Palmer would have given City a half-time lead, too, only for Luban’s outstretched leg to divert his low drive wide.
Goalkeeper Cieran Slicker had proved to be a spectator in the first half, but his alertness had not been dulled by the cold and a fine double save was followed by a full-stretch stop from Cannon as Everton came flying out of the blocks in the second half.
However, City came on strong again.
James McAtee called Luban into action with a dipping 20-yard effort, whilst substitute Charlie McNeill flashed an effort inches wide of the left post.
McAtee might have won it when Joe Hodge’s through ball released him, but the striker’s tame shot was easy for Luban, whose own side were restricted to counter-attacks and set-pieces as the clocked ticked down.
A slide rule ball from Sammy Edozie freed Palmer in the dying minutes, but Everton keeper Luban beat his fierce strike away to ensure a keenly fought contest ended all square.
How we lined up
Slicker’s goal was protected by a back four of Robinson, Egan-Riley, Mbete-Tabu and Wilson-Esbrand.
Oduroh sat deepest in midfield, with Robertson and Palmer, the captain, ahead of him, whilst Bobb and Edozie operated on the right and left flank, respectively.
McAtee led the line up front.
What it means
This was only the third time we've dropped points in the league this season and our first draw, but we remain top of the table with 34 points from 14 games.
Second-placed Liverpool are six points behind, but with two games in hand, whilst Everton are third on 25 points.
Premier League Cup action is up next for our U18 side, who travel to Brighton and Hove Albion on Saturday 25 January for a quarter-final tie which kicks off at 11:00 (UK).
We return to league action the following Saturday, with a home game against Middlesbrough that gets under way at 12:30 (UK).