It was nearly a dream start for Nicky Spooner’s side, as a great combined full team press forced a mistake from Everton goalkeeper Joe Hilton.
However, Ronan Darcy was unable to capitalise on the loose ball before Hilton managed to grasp at the ball to save his blushes.
Everton certainly had their chances in the opening ten minutes, with two efforts from Kieran Phillips only inches from finding the target.
Bobby Carroll was next to test the Bolton defence, as he beat his man in the area to drive towards goal, but his eventual shot was deflected out of play.
Blues winger Korede Adedoyin was close to putting the home side into the lead, as his curled right footed shot from the edge of the area had Alexander beaten in the Bolton goal, but flew agonizingly wide.
With five minutes to go in the half and Everton got their goal.
A freekick from Jack Kiersey was looped into the danger area, and Adedoyin rose highest to nod the ball past Alexander into the bottom right corner.
Wanderers nearly responded perfectly with a goal of their own.
Right back Adam Senior jinked past his man on the right flank, to produce a floated ball into the area but Matthew Barnes couldn’t direct his headed effort on goal.
Ten minutes into the second period and Everton had their second through captain Keiran Phillips.
The Toffees skipper was played through one-one-one with Alexander and he slotted the ball underneath the onrushing goalkeeper.
Wanderers came back with a chance of their own, as Barnes struck an effort with venom from ten yards out but his effort was wide of the target.
Adedoyin was causing problems for Nicky Spooner’s side again.
This time, he made his way into the middle of the pitch and struck a thunderbolt like strike from 18 yards, forcing Alexander to make a magnificent diving save to his right.
Matthew Barnes nearly had a way back into the tie for Wanderers, as he sprinted down the left side of the Everton half, beat two men and flashed his shot perilously close the far corner.
A defensive mix-up by the home side saw the ball fall to second half substitute Demarlio Sterling.
He played into Barnes, but again his well hit shot was just off target.
Everton made it three in injury time as an Adedoyin cross into the danger area found substitute Simms, who slotted home Everton’s third.
Wanderers XI: Alexander, Senior, Edmundson, Smith, Hartshorne, Boon, Graham, Jones-Griffiths (C), Barnes, Darcy, King-Harmes.
Substitutes: Richards, James, Sterling, Osigwe, White.