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Camp kept out a stoppage-time penalty from Nacer Barazite and then turned away a header from Emanuel Villa, who had earlier scored at both ends.
But Derby thought they had won it when Miles Addison headed in a Kris Commons corner only for referee Stuart Attwell to disallow the goal.
The game ended in confusion and the Nuneaton official was the centre of attention after sending off Forest's Lewis McGugan for a tackle from behind on Paul Green and booking seven other players in a game which provided no hint of the late drama that followed.
The first half was virtually devoid of incident but the contest, which was the first between the East Midlands rivals for four years, finally came to life when Forest went ahead in the 55th minute.
When a corner was only half cleared, Luke Chambers fired in a right-foot shot which Stephen Bywater palmed out but the ball struck Villa and cannoned into the net.
The Argentine striker made amends 11 minutes later when a Commons free-kick was flicked on by Barazite and Villa turned the ball past Camp from close range.
Forest were reduced to ten men when McGugan went through Green, although the decision to show the midfielder a straight red looked harsh.
But even though they had lost one of their most influential players, it was the visitors who looked more likely to snatch victory on the break and the match appeared to be drifting to a draw until it exploded in injury time.
Addison thought he had won it only for the referee to award a spot-kick for a handball, but Camp plunged to his right to deny Barazite and he produced an even better save to keep out Villa's bullet header.
But from the corner, Addison again headed into the net but the referee again cut short his celebrations leaving both teams with a point from a typically hard-fought local derby.