Having toiled for over 80 minutes, Rovers recorded their first home win of the season thanks to Derbyshire's clinical left-foot finish.
A managerial masterstroke saw all three Rovers substitutes combine as Paul Ince got the better of his former Inter Milan employer Roy Hodgson.
Before the game, Ince made one change to the side that lost 4-0 at home to Arsenal last weekend, with Keith Treacy handed his full Premier League debut in place of Steven Reid.
Meanwhile, former Blackburn boss Hodgson stuck with the same starting eleven that beat Bolton last time out.
On an unseasonably hot day, both sides started the game with plenty of attacking intent. After just four minutes, Fulham's Simon Davies found space on the right, his low centre was flicked goalwards by Andy Johnson, but Paul Robinson made a stunning reaction save.
On eight minutes, Stephen Warnock's free-kick to Jason Roberts was headed back into the path of the advancing Keith Andrews, whose first-time volley brushed the outside of the net.
Moments later, Roberts almost capitalised on John Paintsil's misplaced header, but his early effort sailed wide of the far post.
Rovers continued to dominate inside the opening quarter of an hour, with Andrews firing over and a Morten Gamst Pedersen free-kick causing confusion in the Fulham defence.
As the half progressed, Bobby Zamora twice headed over from Fulham free-kicks, while Roque Santa Cruz's crisp strike was well kept out by Mark Schwarzer.
The closest either side came to breaking the deadlock arrived five minutes before the break, when man-of-the-match Brett Emerton robbed Danny Murphy in midfield, before curling a delightful effort onto the top right-hand corner of the post from the edge of the Fulham box.
The start of the second half failed to match the same intensity as the first, with neither side registering an effort on goal in the opening 15 minutes.
After finding himself clean through on goal, Johnson had an excellent opportunity to open the scoring on 63 minutes, but the former Everton forward was again denied by a superb Robinson save.
Rovers rang the changes, with Carlos Villanueva introduced for his Premier League bow and the Chile international almost made an immediate impact after a neat one-two with Andrews.
But it was another substitute who stole the headlines at Ewood Park. On 84 minutes, Villanueva's floated pass was headed down by Santa Cruz and Derbyshire finished with aplomb from inside the box.
Villanueva almost put the icing on the cake with a sublime left-foot strike late on, but Rovers held out for a deserved win.