The Reds' promotion push had stuttered recently, but Derbyshire's 25-yard stunner secured a hard-fought victory that followed up the Boxing Day success over QPR.
Promotion rivals Leeds looked to have secured a point when Ross McCormack fired home in the 83rd minute to cancel out Greg Halford's first-half header - but Derbyshire came up with his match-winning moment just a minute later.
It left Forest only five points behind second-placed Derby in the Sky Bet Championship table.
Leeds almost made a nightmare start as Tom Lees fed a short back pass to Paddy Kenny in the first 30 seconds, leaving Halford to chase through. The keeper just managed to beat the striker in the race for the ball, but took a clattering for his trouble, as Halford - quite fairly - slid in to challenge strongly.
Jamie Mackie fluffed his lines when Andy Reid had picked him out with a clever pass, with the former QPR man failing to make proper contact with a shot with the goal at his mercy.
But when Michael Brown brought down Reid crudely for the second time in the game in the 23rd minute - the Leeds man was booked - Forest inflicted further punishment.
Reid regained his feet to deliver a precise ball to the far post, where Halford rose to plant a towering header back across goal and into the net.
Two minutes later and it might have been 2-0 to the home side, with Reid seeing a spectacular dipping shot skim the roof of the net.
Following more good work from Reid, Radoslaw Majewski's near-post shot was pushed away well by Kenny.
Matt Smith could have done better with a header at the other end, which he flashed wide of the upright having risen unchallenged.
Leeds were clearly aware of the threat posed by Reid, who was clattered for the third time in the game, this time by Rodolph Austin, who was also booked.
After winning possession wide on the left in the second half, Mackie embarked on a driving run, before feeding Djamel Abdoun on the right side of the box, where the Algerian forced a good reaction save from Kenny with a rising shot.
Reid was then unlucky not to score when he smashed a spectacular effort against the outside of the post.
And it looked to have been a pivotal moment when Leeds almost immediately charged up the other end of the pitch to equalise.
Following a melee in the box, the ball broke for McCormack and he lashed a low shot inside the post.
But, almost straight from the kick-off, Forest were ahead again, with Derbyshire pulling a goal right out of the top drawer.
There seemed to be little danger when he collected possession 25 yards out, but the striker sent a breathtaking shot high into the corner of the net.