In a keenly contested clash in which both teams failed to truly capitalise on periods of dominance, Paul Harsley’s side went ahead through a Tommy Doyle penalty and a well taken Nabil Touaizi strike.
Everton rallied and though City contained them for much of the second half, the hosts took their chances when they came.
Antony Evans curled a free-kick into the top corner to halve the deficit and, as the clock ticked down, Ellis Simms nodded home an equaliser from close range.
Wind and rain had bludgeoned Merseyside in the afternoon, but the weather settled by kick-off, allowing two sides committed to playing out from the back to exercise their game plans without disruption from the elements.
It made for an entertaining contest, as did the intense pressing, with each team seemingly trying to outdo the other with their efforts.
City settled quicker, with Ian Carlo Poveda tormenting Toffees’ left-back Matthew Foulds during the early exchanges.
One trademark weaving run and pass allowed Adrian Bernabe to hit a fierce 12-yard drive, but Everton keeper Harry Tyrer was equal to it and recovered quickly to prevent Morgan Rogers converting the rebound.
Rogers was also proving difficult to contain down the City left and it was the summer recruit who won the spot-kick, as Ryan Astley and Dennis Adeniran both tried to stop him in his tracks.
Doyle dispatched it with aplomb, firing low and hard into the bottom left corner to maintain his scoring form after his goal against Bradford City in midweek.
Speculative efforts had been as good as Everton could muster up to that point, but they rallied and inspired by Anthony Gordon’s trickery, came on strong before the break.
City’s defence held firm, however, though Bazunu had to make a smart stop from the lively Evans.
The break came at the right time for Harsley’s youngsters, who restarted strongly and doubled the lead four minutes into the second period.
Poveda was the architect, sliding the ball through for Touazi, who swept his first-time effort into the far corner.
City were looking comfortable but a free-kick on the edge of the area allowed Everton a way back into the game and Evans picked out the top left corner to give Bazunu no chance.
The game ebbed and flowed from there, with both defences largely untroubled, but, as in the first half, Everton gained some momentum.
The unmarked Ellis Simms headed over as the hosts signalled their intent and nine minutes from time he was in the right place to nod home a rebound that fell kindly for him after Gordon cannoned a 20-yard effort off the crossbar.
City responded in kind in the closing minutes, but were unable to find a winner despite substitute Jayden Braaf’s best efforts.
What it means
This was City's second draw of the campaign, which leaves us on five points and in 11th place in the Premier League 2 after seven games.
How we lined up
Bazunu was in goal and shielded by a back four of Alpha Diounkou, Rowan McDonald, Yeboah Amankwah and Nathanael Ogbeta.
Iker Pozo sat deepest in midfield, with Doyle and Bernabe ahead of him.
Poveda and Rogers operated on the right and left flank respectively, with Touazi up front.
With an international break on the horizon, we have to wait three weeks until our next Premier League 2 game on Saturday 19 October, when Brighton and Hove Albion visit the Academy Stadium.
However, our U19 squad will be in UEFA Youth League action before then.
We face Dinamo Zagreb at 3pm on Tuesday 1 October at the Academy Stadium. Like City, who beat Shakhtar Donetsk 3-1, the Croatian’s won their opening game, beating Atalanta 1-0.