A team featuring several summer signings, including Josh Bowler and Lewis Gibson, along with Swansea City target Callum Connolly controlled the game against the Welsh club.
But the goals both came from familiar faces with striker Bassala Sambou notching the first just before the break, and experienced left-back Luke Garbutt adding the second from the penalty spot on 64 minutes.
On loan Wolfsburg forward Anton Donkor was among the substitutes named to face the Dafabet Welsh Premier League club.
Highly-rated Bowler, signed for £4.25m from QPR, had a lively game, going close to scoring on a number of occasions. While Sambou, signed last summer from Coventry City, also had a clutch of opportunities to increase the scoreline.
Nathan Woodhead should have made it three near the end but missed the target after Bangor City keeper and former Blues academy player Connor Roberts missed a clearance.
And from evertonfc.com:
Bassala Sambou had a great chance to open the scoring in the 10th minute when he ran onto a superb through pass from Beni Baningime but the centre-forward couldn't find the finish.
The closest that the League of Wales side came to scoring in the opening 45 minutes was a long-range, looping volley from player-manager Gary Taylor-Fletcher that took a deflection and was safely gathered underneath the crossbar by Louis Gray.
The opening goal came in the final minute of the first-half when Gethin Jones clipped the ball into the Bangor area for Sambou to plant a firm header past former Everton academy keeper Connor Roberts.
David Unsworth made a plethora of changes as the second period progressed but it didn't affect Everton's general control of the game, with Baningime once again impressive in the middle of the park.
Calum Dyson fired over from a tight angle and Sambou poked a close-range effort narrowly wide as the Toffees pressed for a second goal.
The advantage was finally doubled in the 65th minute. Harry Charsley was upended inside the box and Luke Garbutt sent Roberts the wrong way from the penalty spot.
Nathan Broadhead came within a whisker of a third Everton goal when he eluded the keeper on the edge of the area but curled his snapshot just wide of the target.
Everton U23s:Gray, Jones, Garbutt, Baningime, Connolly, Gibson, Bowler, Charsley, Sambou, Evans, Dyson.
Subs: Foulds, Renshaw, Feeney, Grant, Broadhead, Markelo, Donkor.