Enzo Maresca’s side looked to be heading for a frustrating draw until Joe Anderson tripped D'Margio Wright-Phillips in the final minute and Doyle showed nerves of steel to fire the spot-kick straight down the middle.
It was relief for City, who were on the front foot for much of this tight contest, but had seen Sam Edozie’s early strike cancelled out by Ellis Simms’ close-range finish.
Maresca’s youngsters started brightly and took the lead when Edozie scored his third goal in two games with a deflected drive that wrong footed Everton goalkeeper, Harry Tyrer.
However, the Toffees responded quickly and levelled when Simms pounced to tap a loose ball into an empty net after James Trafford was unable to claim Rhys Hughes’ hopeful cross.
City were then left breathing a sigh of relief when Matthew Pennington was flagged offside after nodding home from a well worked corner routine.
The game gradually opened up and but for a combination of wasteful finishing and good goalkeeping, a cagey contest could well have been a high scoring affair.
Trafford denied Hughes with a strong one-handed save, whilst the unmarked Ryan Astley headed over from six-yards for Everton and at the other end, Tyrer parried Doyle's dipping 20-yard effort before stretching out a leg to keep out Ben Knight’s snapshot.
Both sides left their best efforts until the closing stages.
Anderson fizzed a sweetly struck half volley inches over Trafford's bar and the impressive McAtee spurned a golden chance for City, dragging a shot wide after a smart turn in the area, but it proved inconsequential when Wright-Phillips won the crucial penalty.
Doyle was calmness personified from the spot, letting Tyrer dive to his right as he rolled the ball down the middle to guarantee all three points with virtually the last kick of the game.
How we lined up
Trafford’s goal was protected by a back four of CJ Egan-Riley, Taylor Harwood Bellis, Luke Mbete and Nathanael Ogbeta.
Doyle, McAtee and Felix Nmecha comprised the midfield three, with Alpha Diounkou and Edozie on the wings either side striker Knight.
What it means
City move up to eighth in the Premier League 2 table, with one win, one draw and a defeat on our record from the opening three games.
The EDS are back in action in two weeks time, after the October international break.
We host Leicester City in a Premier League 2 game on Sunday 18 October, with kick-off at 14:00 (UK).