Forest took a first-half lead through Nicky Southall and looked to be heading for an easy victory before Stock's superb effort.
Following a short corner Stock curled a left-foot shot over the diving Paul Gerrard, much to the delight of the home crowd.
Forest had threatened to run away with the game in the first half and almost took a third-minute lead when Bournemouth keeper Gareth Stewart spilled David Johnson's long-range effort.
And after Johnson curled a free-kick inches over the bar, the visitors put themselves in front on 19 minutes. Johnson was again involved as he crossed for Southall to bundle the ball in from close range.
The visitors should have doubled their lead 12 minutes before the break when James Perch had a free header from Southall's corner, only for the ball to sail wide of the left hand post.
Three minutes later Johnson was guilty of a gilt-edged miss when his header from three yards was superbly kept out by Stewart.
Bournemouth looked a different side after the break and got their reward through Stock's stunner on 64 minutes.
The hosts took control and Forest keeper Gerrard had to be alert on 73 minutes to keep out Stephen Cooke's side-footed shot.
Two minutes from time Stock tried his luck from distance, before more heroics from the Forest defence kept the scores level with a minute remaining.
Substitute James Keene's shot deflected into the path of James Hayter who saw his right-foot effort kept out by Gerrard.
From the resulting rebound Forest defender John Thompson somehow turned James O'Connor's fierce shot wide.