The visitors began the second period brightly, yet neither side was able to fashion much in the way of clear opportunities.
There was, though, the welcome sight for the Reds of Jayden Danns returning to action after injury, soon after the hour mark.
The forward went close to an immediate impact with 71 on the clock, too.
Bringing a left-wing cross under control in the box, Danns’ drives at goal were thwarted by a defender and then the goalkeeper, while the rebound was put off target by O’Connor.
As time ebbed away and the contest appeared to be petering out, minor chaos unfolded.
Everton had the ball in the net via Rocco Lambert’s finish, only for it to be chalked off due to the referee having already blown for a free-kick to the Blues.
Liverpool lost goalkeeper Davies to a straight red card when he mistimed a sliding challenge on Justin Clarke as he rushed out from goal attempting to clear.
With their allotted pauses in play to make substitutions used up, the Reds could not introduce a replacement ’keeper, meaning defender Mor Talla Ndiaye took the gloves.
The home side were then reduced to 10 men as a result of an ill-judged reaction by Braiden Graham on Joe Upton that led to a fracas.
There were half-chances for both rivals in the closing moments – including a save from emergency stopper Ndiaye – but the points were ultimately shared.
**Team**
Liverpool: Davies, Mabaya (Onanuga, 78), Pitt, Lucky, Ndiaye, Trueman (Upton, 78), O’Connor, Laffey, W. Wright, Figueroa (Danns, 62), Sonni-Lambie (Bradshaw, 68).
Unused subs: Ayman, Misciur, Cisse.
Goal: W. Wright (15)
**Next up**
Liverpool host Leeds United at the Kirkby Academy on matchday two of the new Premier League 2 season next Sunday (August 30).
Kick-off is 1pm BST and the game will be [**streamed live on All Red Video**](https://video.liverpoolfc.com/live-events).