The home side applied some early pressure particularly down the Imps' left hand side, and Henry Smith was busy dealing with Chesterfield's crosses from deep whilst the hosts' centre forward struck wide from distance. But City's youngsters gradually began to impose themselves in midfield with Matt Bowles and Kegan Everington snapping in tackles.
The breakthrough came on just 11 minutes when good pressure high up the pitch allowed Alex Simmons to break free and he finished calmly through the keeper's legs.
Simmons and Rob Smith now began to run at the opposition and Smith beat his man on more than one occasion forcing a couple of corners and smashing a couple of crosses into the box. Kieran Walker found himself in the box and his shot was blocked, then Matt Cotton drove to the byline and his cutback narrowly evaded Kieran Helsdown in front of goal.
Chesterfield remained a threat on the break but the back four marshalled by Callum Ward and Jordon Cooke coped well with the home side's quick counter attacks. More good work from Smith and Cotton down City's left saw a cross overhit and Nick Green arrived just too late in the box.
Then, on the stroke of half-time, the Imps doubled their lead; Cotton stealing the ball and quickly finding Simmons who immediately released the breaking Smith who finished well to take the youngsters into a deserved half-time lead.
Chesterfield made changes at the break and came out to press the Imps and they were rewarded when Walker was harshly judged to have tripped his marker in the box. Henry Smith guessed correctly but couldn't prevent the equaliser.
The game was now a real cup tie and the Imps hard to overcome this setback, and work hard to take control again in midfield.
More pressure and more breaking midfielders soon resulted in more chances as Smith and Bowles went close, then on 70 minutes a whipped free kick from Cotton found Helsdown unmarked and he narrowly missed the target. Minutes later Smith smashed against a post and the Imps continued to press.
In the dying minutes Chesterfield threw everything forward and following a scramble in the box, Walker cleared off the line. But the youngsters held on for a deserved victory after a very hard working performance.
The cup action continues when they travel to Bury on Saturday in the Youth Alliance Cup before the short trip to Boston United in the FA Youth Cup next week.