Magath's young side looked worryingly frail at the back and fell apart as Derby ran riot in the second half with Chris Martin scoring twice.
Jamie Ward gave Derby a half-time lead and although Scott Parker equalised, Martin's double and strikes from Craig Bryson and Simon Dawkins made it a miserable day for relegated Fulham and Magath.
Despite losing the opening three games, Fulham made only one change, while Derby made two with 34-year-old midfielder John Eustace coming in for his first appearance since March in place of Will Hughes.
Given those poor results, it was not surprising that Fulham started nervously, and Derby had a chance in the third minute when Cyrus Christie found Johnny Russell just inside the area, but the Scot volleyed over.
Parker's measured passing got the Londoners moving but Derby had another opening in the 13th minute when the ball dropped invitingly to Christie, but he shot straight at Jesse Joronen from 15 yards.
Fulham were being stretched by Derby's movement, and in the 23rd minute they were behind once again when Russell crossed from the right and Ward steered a volley from eight yards into the roof of the net.
The visitors needed a spark of inspiration, and Ross McCormack nearly supplied it in the 37th minute with a shot from just inside his own half which Lee Grant had to back-pedal to take under his crossbar.
But Derby had been the better side and they came close to scoring again in the 51st minute when Ward crossed from the right touchline and Richard Keogh headed over from eight yards.
Fulham had created little but they were level in the 54th minute when McCormack chipped the ball in and Ryan Williams laid it to Parker who placed a low shot from 15 yards inside Grant's right post.
It stung Derby into a rousing response that brought them two goals in three minutes to leave Fulham sliding to another defeat.
First, Jeff Hendrick played in Russell on the left in the 59th minute and his ball back across was swept past Joronen by Bryson.
Fulham's defence was exposed again in the 61st minute when Martin was allowed to turn just inside the right side of the area and the striker arrowed a low shot across the keeper for his first Championship goal of the season.
The closing minutes were a nightmare for Fulham as Martin tapped in after Dawkins hit a post in the 87th minute before Dawkins strode through another gaping hole in the defence to slide in Derby's fifth.