Pools progress into the next round of the Papa Johns Trophy as Maty Daly solo goal give Sweeney’s side the victory.
Pools dominated possession from start to finish and had the majority of the chances throughout the game. The first chance came from Tom Crawford just after two minutes as his strike on the edge of the box was blocked.
Right towards the end of the first half, a Neill Byrne header from the corner was blocked from close range which ended a first half of very little chances and very little action.
The second half became a little livelier. Straight after the break, Ogle found himself free at the backpost and his effort from close range was blocked.
Just five minutes later, Tom Crawford had another chance on the edge and it was saved by Tyrer.
Everton had their best opportunity on 55 minutes. Dobin ran through one on one and lobbed Mitchell but luckily for Pools hit the cross-bar.
A double change for Pools changed the game as Molyneux and Daly came on to make an instant impact.
Maty Daly on 71 minutes danced through the Everton defence, round the keeper and smashed the ball home.
Pools were able to see out the rest of the game, late chance for Molyneux threatened for a second but Pools progress in style.
Mitchell; Jones, Francis-Angol( Molyneux), Byrne, Odusina, Ogle; Crawford, Smith, Shelton; Goodwin(Daly), Grey(Cullen)
Subs: Killip, Hendrie, Featherstone, Daly, Molyneux, Cullen, Fondop