The Gunners, who had gone in front through Nikolaj Moller, were reduced to ten men in the 7th minute when Karl Hein fouled Nmecha as he raced in on goal.
The midfielder dusted himself off and equalised around 20 minutes later to ensure we went in all square at the break.
The visitors took an early lead when Moller's 6th minute effort squeezed agonisingly over the line after Taylor Harwood-Bellis had blocked Flo Balogun's initial effort on goal.
We immediately began searching for a way back into the game, and almost found it within a minute when Nmecha beat Hein to the ball and was caught by the goalkeeper just outside the box.
The visiting stopper was given his marching orders for the challenge, with the Gunners forced into putting outfield player Taylor Foran between the sticks for the remaining 83 minutes.
With the man advantage, City began to enjoy the majority of the play, and were almost level just after the 20-minute mark when Harwood-Bellis’ cross from the left following a corner was sent just over by Morgan Rogers on the volley.
But we didn’t have to wait much longer for the breakthrough, with Nmecha racing on to a clever reverse pass from Rogers down the left of the box before calmly slotting home a 24th minute equaliser into the far corner.
Arsenal put bodies behind the ball and looked to frustrate the Young Blues with two banks of four and Moller pressing high on our backline, but we continued to find space in dangerous areas thanks to some crisp passing and clever movement.
We were almost ahead just after the half-hour mark when Rogers beat his man and drilled a vicious low ball across goal, but neither Tommy Doyle nor the onrushing Adrian Bernabe could get a clean contact at the back post.
And two minutes later skipper CJ Egan-Riley almost got himself on the scoresheet when he ghosted into the box, but his volley was well saved by the feet of makeshift stopper Foran.
And it almost paid dividends within the opening ten minutes of the half, when Bernabe’s delightful trivela cross from the right found Delap, whose effort was pushed just wide by Foran.
However, that crucial second soon followed from the boot of super-sub McAtee just before the hour.
The midfielder picked up play just outside the box before calmly placing a low effort through a crowd of bodies and inside the near post.
The game continued to ebb and flow after we had taken the lead with McAtee almost turning provider for Delap just before the 75-minute mark, but Foran once again got down well to his left to deny the forward.
But the game was far from over, with Balogun probably feeling like he should have at least hit the target when sent clean through with 12 minutes to go.
The forward looked to chip James Trafford, who had done well to come quick off his line and narrow the angle, but his dinked effort had too much on it to bring the visitors level.
The game was finally put to bed when Delap got the goal his performance deserved, finding a pocket of space just inside the box before smashing the ball into the top corner to give us a two-goal cushion.
Substitue Dionkou then added further gloss to the scoreline when he slid home at the back post to put away Bernabe's low cross.
A hard-fought and well deserved three points for Enzo Maresca’s men, who now sit just three points off the top of the Premier League 2 table.
How we lined up
Trafford’s goal was protected by a back four of Egan-Riley, Burns, Harwood-Bellis and Luke Mbete.
Claudio Gomes screened in front, with Doyle and Nmecha given licence to push forward and support the front three. At the sharp end, Bernabe and Rogers started on the flanks with Delap leading the line for the Young Blues.
What it means
The win pushes us up to fifth in the Premier League 2 table and just a single point outside of the top four.