Tuesday's result at Pride Park leaves Forest still fearing relegation from the Championship.
Substitute Buxton rose highest at the far post to nod in Ben Davies' cross and stun Forest five minutes into time added on.
Buxton's winner came soon after Forest had been reduced to 10 men, with former Rams striker Marcus Tudgay shown a second yellow card for a lunge on Ben Davies.
The game had seemed destined to end as a draw, until a dour but passionate encounter burst into life in the closing stages.
Forest had experienced a resurgence before their short trip down the A52, but this defeat will leave them looking anxiously over their shoulders.
Derby look destined for a mid-table finish, but this dramatic victory game them their first double over their nearest rivals for 40 years.
Forest boss Steve Cotterill urged his side to show cool heads ahead of the game, but they had two players booked in the opening 20 minutes, with central midfield duo Adlene Guedioura and Guy Moussi going into Andy D'Urso's notebook following fouls on Nathan Tyson and Steven Davies respectively.
Steven Davies had already been booked by that time after a needless challenge on Andy Reid.
The pace was frantic, but there was a shortage of quality from both sides. Former Forest man Tyson had an opportunity to open his Rams account after 27 minutes but the striker was indecisive and the chance was gone,
In-form Derby striker Steven Davies drilled a left-foot strike over the crossbar seven minutes before the break and the Rams were almost caught out at the other end when Jason Shackell's poor header fell nicely for Tudgay, but the former Derby frontman poked a tame finish behind Frank Fielding's goal.
Tyson then showed his first moment of quality with a sharp turn and cross for Craig Bryson, but the Scottish midfielder scuffed his shot right on the stroke of half-time.
Rams keeper Fielding breathed a sigh of relief seven minutes into the second half when he flapped at a cross and Moussi's goal-bound shot was diverted for a corner by a retreating defender.
There was plenty of endeavour but both sides were devoid of ideas, although Tyson tried his luck after cutting in from the right but his left-foot strike flashed wide.
Forest keeper Lee Camp then misjudged a Ben Davies cross but scrambled across to palm the ball away. Then tensions almost boiled over moments later when Dexter Blackstock scythed down Ben Davies, resulting in a melee just in front of the technical areas but only Blackstock booked.
Rams skipper Shaun Barker was then carried off with what appeared to be a serious injury and Forest were almost in fronts moments later when Tudgay headed Andy Reid's inviting free-kick just wide.
But Tudgay was then given his marching orders for a wild lunge on Ben Davies and there was more drama to come as Buxton headed home Ben Davies' inviting free-kick to secure a dramatic victory.