But the visitors claimed two goals in the final five minutes with Delap also being sent off for a second yellow card as Derby fought back from 3-1 down to take a point back to the East Midlands.
With new head coach Maresca looking on after completing his quarantine precautions, City went into the game buoyed by last Tuesday’s fine EFL Trophy Group E win at Mansfield.
That belief and momentum was evident from the off as City took the game to a talented Derby outfit.
On 10 minutes former Rams starlet Liam Delap almost gave us the perfect start. The striker latched onto an errant back pass and neatly switched inside before firing a stinging shot which keeper Manny Idem pushed behind.
More indecision in the Rams backline almost saw Delap make his presence felt again before City’s bright start was rewarded with the opening goal on 23 minutes.
Winger Sam Edozie was the provider, his pace opening up space on the left flank before his smart cross was met by James McAtee who drilled home a fine finish.
Derby were a threat on the break however and it needed a timely block from sub Nat Ogebta to take the sting off a goalbound Josh Shonibare effort after he had arced round the edge of the box.
It was City though who struck again with a quite brilliant Delap goal just before the break.
The striker first showed his skill by gathering and then dinking the ball over the Derby defence before opening up space and finishing in style for his third goal in two games.
However, the visitors served notice of their quality by narrowing the deficit in first half injury time, the ever dangerous Shonibare squeezing a shot past Cieran Slicker into the corner of the net from 18 yards.
That goal imbued Derby with an extra spring in their step and only a last-ditch block by Burns prevented Shonibare levelling affairs on the hour.
Derby keeper Idem then produced a stunning one hand ed save to deny Delap a second as both sides stepped up the intensity.
And it was City who claimed the all-important next goal thanks to a piece of McAtee brilliance.
The midfielder drilled home an exquisite free-kick after Delap had been upended just outside the box.
That looked to be it - only for Derby to stage a dramatic late fightback with City suddenly on the back foot.
Frist full back Callum Minkley struck on 87 minutes to narrow the deficit. Then, after Delap was dismissed for a second booking, 60 seconds later Archie Brown's shot was deflected by Luke Mbete past Slicker to draw the visitors level.
How we lined up
Cieran Slicker was in goal and shielded by a back four of Sammy Robinson, Finley Burns, Luke Mbete, and Josh Wilson-Esbrand. CJ Egan-Riley was the holding midfielder with James McAtee and Oscar Bobb also in the engine room.
Enzo Maresca’s side are back in PL2 action this Friday evening when we make the short trip to Lancashire to take on Blackburn Rovers.
Kick-off is 7pm.