Reece James gave the young Blues their opening Premier League 2 win of the season with a smart smash and grab shot from close range on 64 minutes.Luke McCormick snatched the second, deep into injury time, tucking the ball home smartly from eight yards.
The Blues drew their opening fixture, an 0-0 away draw at Manchester City last week.
This was a tired performance from the kids and boss Joe Edwards can take comfort that his half time team talk awakened the youngsters from the slumber they were in in the first.
Joseph Colley came to the rescue of the young Blues on five minutes, throwing himself to the near-post, goal-bound half-volley from Timi-May Elsnik.
A pulsating lung-busting run by Dujon Sterling on six minutes, almost reaped dividends as he crashed to the ground in the Derby penalty area, but referee Gary Parsons saw that the right-back ran out of steam.
A scintillating break, orchestrated by Ethan Apadu and Cole Dasilav threatened the Derby goal, with Luke McCormick almost snatching a near-post half-volley, but the ball was deflected away for a corner.
A brilliant parry by goalkeeper Marvin Bulka, 16, prevented the Rams from taking a lead with two minutes of the first half remaining.
The 6ft 5in tall polish stopper dived low to his right to clear a fierce daisy-cutter from Kellan Gordan.
Joe Edwards refrained from making any half-time changes. Derby replaced George Thorne for Joe Bateman.
But while the Blues kept the ball better, they failed to thrash the Derby gol.
Edwards opted to make his first change on 61 minutes bringing on Miro Muheim for Jacob Maddox and Jordan Houghton for Ruben Sammut. Derby replaced Jason Shackall for Alex Cover.
The changes reaped dividends almost immediately when Reece James tucked the ball home from close range from a regulation corner on 64 minutes.
Derby’s final substitution took place with 18 minutes left with Offrande Zanzala being replaced by Luke Thomas. Edwards brought on Joshua Grant for Cole Dasilva a minute later.
Derby were desperately unlucky not to equalise on 84 minutes but Emil Jakobsen saw his deft chip over Bulka rebound off the crossbar and cleared.
Rams left back, Calum Macdonald, already yellow carded for a foul, lost his head on 88 minutes, needles handling the ball when it was going out of play. Parsons had no option but to show a second yellow nod then a red card.
Any recovery from then on was forlorn and fruitless.
Luke McCormick smacked home the second goal deep into injury time.
Chelsea: Martin Bulka, Dijon Sterling, Reece James, Joseph Colley, Ethan Ampadu, Ruben Sammut (capt), Isaac Christie-Davies, Luke McCormick, Callum Hudson-Odoi, Jacob Maddox, Cole Dasilva
Subs: Jordan Houghton, James Russell, Miro Muheim, Charlie Brown, Joshua Grant.
Derby: Roos, Stabana, Macdonald, Thorne, Wssell, Shackell, Gordon, Elsinore, (capt), Jakobson, Babos, Zanzala
subs: Cover, Barnes, Bateman, Karin, Thomas
Referee: Gary Parsons