The visitors got their noses in front on two separate occasions in the first half, scoring just before the break after Liam Delap had pulled us level.
But a quickfire goal from McAtee and a Sam Edozie penalty saw us take the lead before the former bagged his brace late on.
In a cagey first half, it was City who produced more of the chances, with McAtee's stinging shot brilliantly saved by Palace keeper Whitworth, before Delap fired over from inside the area.
Whitworth was in inspired form, showing great reactions on two separate occasions to deny Edozie from close-range.
And the away side made it count when striker Robert Street rose highest to head home past Van Sas for the game's opening goal.
Undeterred, Brian Barry-Murphy's side responded almost instantly when Delap fired past Whitworth following McAtee's lovely cushioned header.
But as quickly as we were level, we found ourselves behind again as midfielder Malachi Boateng slotted home on the rebound after the ball bounced back off the post.
City immediately imposed ourselves after the break and got off to the dream start when McAtee fired home from inside the box, bringing us level.
And just a few minutes later we were ahead for the first time in the game, when referee Paul Marsden overturned his initial decision after discussions with his linesman and pointed to the spot after substitute Tai Sodje was brought down in the area.
The responsibility was taken up by Edozie and the winger made no mistake, firing a powerful effort into the top corner to hand us the advantage.
We managed to control the game for much of the second half after going ahead and McAtee put the result beyond doubt when he poked the ball home for our fourth and final goal of the afternoon, taking his own PL2 tally up to an astonishing nine strikes in five matches.
HOW WE LINED UP
WHAT IT MEANS
A win sees us stay top of the Premier League 2 table, although we are now three points clear of closest competitors Brighton.
It also continues our unbeaten start to the season under Brian Barry-Murphy.
The EDS will take on Doncaster Rovers in the Papa John's Trophy on Tuesday.
Kick-off is at 7pm (UK) at the Keepmoat Stadium.