The Rams got themselves back into it with two goals in five minutes to draw level, before Carlos Borges netted a late strike five minutes from time which looked to be enough for Vicens' team.
However, there was a sting in the tail as Osazee Aghatise equalised deep into injury time to ensure City only left with a single point.
Our first chance of the afternoon fell the way of Oscar Bobb, as the Norweigan linked up with Sodje before striking his effort against the post.
The rebound fell to the feet of Borges, however the winger couldn't divert his effort from close range on target.
After a dominant start with the ball City found the opener with 25 minutes on the clock as Borges set up the prolific Sodje, who headed home for his 18th league goal of the season.
10 minutes before the break captain, Kwaku Oduroh came close to getting his name on the scoresheet, as his powerful effort from the edge of the box forced a good save out of the hosts' trialist goalkeeper.
Vicens' side continued their dominance into the second half, and we doubled our lead just two minutes after the restart as Robertson scored his eighth U18 Premier League North goal of the season.
Despite our two-goal advantage the home side turned the game on it's head just before the hour mark, as two trialists both found the net in the space of five minutes to level things up at 2-2.
After the setback the City youngsters began their quest to regain the lead, and we nearly had it with 15 minutes left to play.
A dangerous free-kick from the right fell to the feet of Sodje inside the six yard-box, however the number-nine had his goal-bound effort well blocked by the Derby defence.
If Vicens' team were to regain their goal difference lead at the top of the U18 Premier League North table, three points was a must in this one and City thought they had this five minutes from time as Borges regained our lead.
However, the Rams once again cancelled out City's lead as an injury time goal from Osazee Aghatise ensured the points would be shared in dramatic fashion.
HOW WE LINED UP
Tai Sodje led the line up-front.
WHAT IT MEANS
The draw means City remain second in the league table, two points behind leaders, Manchester United with seven games to go.
Vicens' side return to U18 Premier League North action on Saturday 20 March, as we host Leeds United at the Academy Stadium.