The emphatic victory also means we remain five points clear at the top of the Premier League 2 table.
Maresca's side got off to the perfect start as we took the lead inside two minutes.
A nice move allowed McAtee to find Palmer on the right, who cut into the West Ham box before curling his effort into the bottom corner for his sixth league goal of the season.
McAtee - who proved provider in the first goal - had a chance of his own 15 minutes later, as the midfielder weaved his way past his man before hitting an effort from the edge of the box straight at Joseph Anang in the Hammers goal.
After a slow start the visitors did begin to get a foot-hold on the game, however a resolute City defence made it difficult for the Hammers to create any real opening.
West Ham did have their best chance of the match just moments before half-time, as the ball was pulled back to an unmarked Conor Coventry on the edge of the box.
Fortunately for City, his effort was denied by a fantastic last-ditch block by Callum Doyle to ensure we headed into the break with our goal advantage.
Into the second half, and we began it just as we started the first as Palmer netted his, and City's second a minute after the restart.
After our first two goals were both created and finished with class, it is fair to say our third came somewhat fortuitously.
A curling Tommy Doyle corner cannoned off West Ham man Josh Okotcha and past Anang into the net to extend our lead to three.
One man who had been fairly quiet by his standards was league top scorer Delap. However, the City number-nine finally had his goal just after the hour mark.
The forward broke free beyond the Hammers defence and smashed home into the bottom corner for his tenth goal in five games.
City were not done there though, as Palmer capped off a superb showing by sealing a well deserved hat-trick.
The winger danced past his man, before side-footing into the far corner to cap off a magnificent display at the Academy Stadium.
HOW WE LINED UP
Liam Delap led the line up-front.
WHAT IT MEANS
The victory means City stay top of the Premier League 2 table, five points clear of second place, Blackburn Rovers.
Our EDS return to league action on Monday 15 March, as we host Southampton at the Academy Stadium. Kick-off is 14:00 (UK).
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