The hosts appeared to be cruising after Moussa Dembele's first Fulham goals fired them into a 2-0 lead shortly before half-time.
But Chris Martin pulled one back from the penalty spot before the interval and the Cottagers capitulated after the break as goals by Johnny Russell, Jeff Hendrick and two from Simon Dawkins in a whirlwind 20 minutes sent the Championship leaders through.
"The goal just before half-time gave us a lifeline," said Rams boss McClaren
"And at half-time the players wanted to do something about it
"The second half was more like us, we showed good character and played some good football
It was a devastating period."
Dembele opened his account in the 27th minute when he intercepted Craig Forsyth's backpass, rounded goalkeeper Kelle Roos and rolled the ball into an empty net
Worse was to follow for Derby in the 45th minute when Roos inexplicably passed the ball to Omar Mascarell, who was promptly robbed on the edge of the box by the lurking Bryan Ruiz to tee up Dembele for the second.
However, the spirit of generosity quickly spread to the Fulham defence when moments later, in first-half stoppage time, Tim Hoogland handled Mascarell's free-kick and Martin dispatched the penalty
It proved a pivotal moment and fired-up Derby drew level within two minutes of the restart when Dawkins reached the byline and cut the ball back for Russell to rifle home from close range.
They took the lead in the 54th minute, Dawkins crashing in a superb angled drive from 20 yards, and six minutes later Forsyth flicked on Craig Bryson's cross to leave Hendrick with a simple finish from six yards out
The fifth arrived when Russell crossed from the right and Dawkins found the net with an extravagant backheel flick to put the seal on a stunning comeback.
Fulham were thumped 5-1 at Derby under Felix Magath in August but have looked a different side since caretaker boss Kit Symons took over.
"We scored two tonight so that's progress," smiled Symons
"In the first half we were well and truly in it, but the goal on the stroke of half-time gave Derby a huge lift and top teams don't need lifts like that.
"We nullified them in the first half but the second half was a different story and Derby punished us."
Despite having previously guided Fulham to five wins from the previous eight matches, Symons has yet to be named the club's permanent manager, but he added: " I don't think one result will hamper my chances."
McClaren agreed, saying: "I thought Fulham were excellent, and if they don't give him the job tomorrow I'll be very surprised."
Source : PA