It could have been worse for Town as well as Gareth McAuley allowed himself to be robbed by Dele Adebola in stoppage time, and hauled the big forward back just outside the box to get himself sent off, but the hosts hung on for a draw.
Town had a dream start when they went ahead for the first time this season as Carlos Edwards' long throw was flicked on by the recalled Jon Stead and Leadbitter volleyed home from ten yards.
In a frantic opening spell, Joe Garner shot narrowly over and David McGoldrick headed wide as Forest pressed for an immediate reply, while Alan Quinn fired a loose ball over for the Blues.
Forest almost grabbed a freak equaliser when Dexter Blackstock blocked a Liam Rosenior clearance and it looped over Richard Wright but dropped wide of the goal.
Town could have snatched a second when Rosenior got to the byline from an Edwards pass and lashed in a low cross which narrowly evaded both Jon Walters and Stead as they came flying in.
Camp beat away a fierce cross-cum-shot from Edwards on the stroke of half-time and at the interval Forest boss Billy Davies sent on Adebola for Blackstock, who had taken a couple of knocks.
Damien Delaney curled a shot not far wide from 20 yards as Town started the half well, but their lead was lost on 59 minutes when Earnshaw - only on the field for a minute - dummied a ball forward, took Adebola's return and skipped into the box to fire past Wright.
Roy Keane made an immediate double change, sending on Jack Colback and Jaime Peters for Quinn and Edwards, and Peters tried to spark his side into life with a run and shot which deflected narrowly wide.
McGoldrick drove a fierce shot across the face of goal after tricking his way past home skipper Alex Bruce, but by and large clear chances were few and far between on a surface made greasy by persistent rain all evening.
Stead fired over for Town and Lee Martin curled an effort wide for Town as the hosts pressed, and Delaney wasn't too far off target either with a low shot which deflected narrowly wide.
That led to the best chance of a winner for the hosts as Martin's ensuing corner was firmly met by McAuley's downward header, but Forest had two men stationed on the line and one of them, Paul McKenna, volleyed clear.
Camp saved a long-range free-kick from Leadbitter which skidded awkwardly off the turf, but then Forest almost snatched it in the last minute of regulation time after McAuley's blunder.
Given ample time to play the ball forward the Northern Ireland international dawdled, allowed Adebola to rob him and then hauled him down just outside the box to earn an obvious red card, but the wall blocked the ensuing free-kick.