The visitors, who had won their previous five matches to surge up the table, fell behind to Darren Ambrose's first-half free-kick.
But McGoldrick, the summer signing from Southampton, grabbed his second goal of the season to salvage a draw.
Forest goalkeeper Lee Camp was given a warning of what was to come when he kept out a fierce free-kick from Ambrose in the first five minutes.
Yet the in-form visitors were the slicker side in the opening stages, with the lively Nathan Tyson heading their first chance over the bar from Chris Cohen's cross.
Tyson then got behind a static Palace rearguard when he latched on to Paul McKenna's ball over the top but could not guide his shot goalwards.
Palace threatened more as the first half wore on, Camp tipping Danny Butterfield's header away and Shaun Derry shooting over the bar.
They were dealt a blow when on-loan West Ham striker Freddie Sears, still looking for his first goal of the season, limped out of the action with a groin injury.
Substitute Victor Moses almost scored with his first touch, but his close-range volley was deflected wide.
Palace did go ahead five minutes before the interval when Ambrose blasted his free-kick past Camp and in off the underside of the bar.
Tempers flared moments later when Clint Hill appeared to swing an arm at Paul Anderson, but the Palace left-back escaped with a yellow card.
Forest manager Billy Davies was clearly furious at the incident, while winger Anderson had to be substituted.
But the visitors calmed down at half-time and pulled themselves level three minutes after the restart.
Lewis McGugan swung over a cross from the right, and McGoldrick slid in unchallenged to steer the ball past the helpless Julian Speroni.
Camp pulled off a finger-tip save to deny Ambrose a second goal with a close-range volley on the hour mark.
At the other end, Tyson met a free-kick from Cohen but planted his header wide.
Former Forest striker Stern John almost found the net when Wes Morgan's clearing header found him 30 yards out, but his shot flew inches wide.
John was denied a winner by the impressive Camp in stoppage time when his shot was turned around the post.