Goals in quick succession from Herbie Kane and Corey Whelan put Neil Critchley's team in charge midway through the first half at Prenton Park.
Rhian Brewster then added to the hosts' tally early in the second period as he produced a marvellous volley and his replacement Yan Dhanda wrapped the points up with a memorable solo goal.
In an open start to the game, the Reds and Blues took it in turns to carve out good chances.
Wilson was unfortunate not to get more purchase on a shot after being fed by Danny Ings inside the box before the Welshman sent a finish from a clipped ball over the top narrowly wide.
As for the visitors, they would have been aggrieved not to make more of an opportunity to break that ended in Liam Walsh overhitting a cross, while Nikola Vlasic forced Kamil Grabara into a smart save shortly after.
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Thankfully for Liverpool, they found their finishing touch before their opponents, and made it count by notching two goals in just three minutes just past the half-hour mark.
The first came when Wilson brilliantly tempted three defenders toward him in the Everton box before teeing up Kane for a powerful close-range finish.
And the U23s captain was at it again straight after the restart, sending a corner onto the head of Whelan, who made no mistake in nodding in.
The No.11 might have had a goal of his own before half-time but saw a deflected attempt set up by Ovie Ejaria dribble agonisingly wide of the post.
The break in play offered Everton a chance to recover from that quickfire double blow, but they were under the cosh again when play resumed.
And the difficulty of trying to subdue to their rivals' potent frontline was underlined in the 53rd minute as Brewster sumptuously volleyed home Kane's cross-field pass to make it three.
The young striker was taken off shortly after, with Dhanda taking his place, but any Evertonians who viewed that move as the Reds taking their foot off the pedal were soon provided with an emphatic response.
Dhanda showed just why he has been deemed worthy of a step up to U23s football this season, picking up the ball up in a deep position and breezing through the Everton defence before cracking a finish into the far corner.
Liverpool: Grabara, Flanagan, Juanma (Johnston, 89), Jones, Whelan, Ejaria, Wilson (Adekanye, 81), Virtue, Kane, Brewster (Dhanda, 67), Ings.
Unused subs: Firth, Masterson.