The young Blues have now won all four games, scoring 17 goals - though the only blot on the copybook was the late sending off of Palmer who was dismissed for a tackle from behind.
City showed signs of attacking promise from the get go - striker Liam Delap ploughed through the visitors’ defence on more than one occasion.
Eventually, his endeavours paid off as he found captain Palmer in the 22nd minute, who used space on the edge of Everton’s box to dink the ball over Jack McIntyre and make it 1-0.
The Toffees responded soon after and almost grabbed an equaliser just 10 minutes later, rattling Cieran Slicker’s right hand post instead.
The Blues, however, retaliated almost immediately, with Bobb converting Lewis Fiorini’s rebounded cross from close range to double the lead.
The second half saw the impressive Delap break through Everton’s defence again and have a couple chances on goal, but McIntyre was always there to pad the striker’s efforts to safety.
In the 80th minute our victory was sealed, however, after Delap’s charge into the box resulted in Palmer finding space. He dribbled past both goalkeeper and a defender on the line to double his tally and make it 3-0.
Four minutes later the captain was shown a straight red for a challenge from behind, and Everton substitute Max Thompson had his long range effort saved by Slicker.
The ten men of City comfortably saw out the time that remained and rewarded manager Gareth Taylor with a well-deserved clean sheet.
Cieran Slicker started in goal, with Sammy Robinson, Finley Burns, CJ Egan-Riley and Oscar Tarensi making up the back four.
Rowan McDonald, Cole Palmer and James McAtee played in the middle of the park, and Lewis Fiorini, Oscar Bobb and Liam Delap provided our attacking force.
After the international break, our Under-18s will welcome Liverpool to the City Football Academy on 14 September.