Impressive in beating Manchester United in the third round, Lampard's young side were the architects of their own downfall in London as Chelsea loanee Fikayo Tomori and Richard Keogh both put through their own net inside 21 minutes.
The host was not immune to horror moments at the back, with Jack Marriott and Martyn Waghorn on target in a thrilling five-goal first half that concluded with Cesc Fabregas restoring his team's lead.
And it proved to be the winner as the upright denied David Nugent late on and left Blues legend Lampard to contemplate the unusual feeling of a Stamford Bridge defeat.
Tomori and Mason Mount were granted special dispensation to feature against their parent club, yet the Rams might have wished that was not the case when Davide Zappacosta's cross struck the former's standing leg and diverted in for the fifth-minute opener.
The inexplicable error was quickly forgotten as Marriott, a scorer against United, capitalised on Gary Cahill's slip to drive an unerring low finish across Willy Caballero.
A stumbling Waghorn passed up a one-on-one chance to complete a quickfire turnaround and Derby punished themselves through more calamitous defending.
In eerily similar circumstances to the first, the experienced Keogh sliced another right-sided Zappacosta cross past a bewildered Scott Carson.
Still, the visitor was just as dangerous going forward as it was in its own box and snatched a second equaliser after 27 minutes, Mount squaring for a Waghorn tap-in.
But it failed to plug the leaks and it was no surprise that Fabregas forced home the third for Maurizio Sarri's side from close range in the 41st minute.
A quieter second half eventually livened up, with substitute Nugent turning the last of three Derby openings into the base of the far post, forcing Lampard to settle for the consolation of receiving the adulation of the supporters, who consistently sung his name.