Cole, who had starred for England’s Under-16s in midweek, earned his reward with a step up, and a typically cool goal, watched from the sidelines by former England striker father Andrew.
However, in a swashbuckling match to delight the fans if not the coaches - City fell two goals behind in the opening dozen minutes - it was Robinson who made the difference against a decent Derby outfit.
His hat-trick did include a penalty that was almost saved by inspired Derby goalkeeper James Severn, but Robinson also crafted the other two Blues goals to earn a deserved ovation at the end.
Derby settled the quicker, though, and a well-weighted long ball out of defence by Alex Witham gave lively County the platform to take a third-minute lead through Kwame Thomas.
When they increased that advantage via prolific and strong striker Callum Ball - who has first-team experience already - again from Witham’s long pass, it looked like City might struggle.
Instead they buckled down and Robinson hit a great shot to pull one back on 21 minutes just after Severn had been forced into a top-drawer save by the menacing Cole
Blues were level from the spot after Cormac Hegarty handled Tom Skogsrud’s cross in the 28th minute, Robinson squeezing the penalty inside Severn’s fingers and his left-hand post.
Seven minutes into the second half, City were ahead for the first time as Robinson slipped the ball through for Cole, who had timed his run perfectly, to stroke past the Derby keeper.
Ball made it 3-3 with a magnificent dipper into Halsall’s top corner, but Robinson was determined to have the last word, firing City ahead again after a neat one-two with Adam Drury.
With Derby ever-threatening - Ball had a rocket of an effort deflected against a post - City needed the 87th-minute fifth from Albert Rusnak, courtesy of Robinson’s surging run, to be sure.
