Summer signings Britt Assombalonga and Matty Fryatt scored the goals as Stuart Pearce's side came roaring back from conceding to Callum Wilson on 58 minutes.
Bournemouth dominated possession but were left stunned as Assombalonga (67) and Fryatt (72) sent their visitors to the top of the fledgling Championship table.
Forest are now one of only four teams in the division to have made an unbeaten start to the campaign.
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