In a game of few chances, both sides had settle for a point with the visitors tightening their grip on a top-six spot.
The draw for Forest, means they have now lost just once in their last 11 league games.
Story of the match
Nottingham Forest went into the game unchanged after the 3-0 victory against Wycombe Wanderers last Saturday.
The visitors were forced into an early change after Steve Cook picked up a groin problem in just the third minute. The experienced centre back was replaced by Kelly.
The first real chance of the game fell to Bournemouth after a short corner from the Cherries allowed Stanislas to have a curling effort whistle just past the post of Forest goalkeeper Brice Samba.
A quick counter-attack for Bournemouth led to a great ball in from Arnaut Danjuma who picked out Shane Long who narrowly headed the ball over the bar.
The first half an hour of the game was an even affair with both sides enjoying good spells but neither able to grab the crucial first goal.
Chris Hughton and his side controlled the last 15 minutes of the first half and looked the most likely to grab the opener after James Garner fired wide after a poor clearance from Cameron Carter-Vickers, but the sides went into the break goalless.
The first 15 minutes of the second half followed the previous 45, with both defences coming out on top and neither side able to create any clear cut chances.
The first effort on goal in the second half came in the 73rd minute when a long raking ball found Anthony Knockaert who brought the ball down but fired well over the bar of Asmir Begovic.
The best effort on goal came in the 78th minute when Filip Krovinovic's corner was met by Glenn Murray at the near post but his glancing header was cleared off the line by a combination of Pearson and Begovic.
Man of the match
James Garner - Nottingham Forest
At the tender age of just 19, the Manchester United loanee had a fantastic performance for the Reds controlling the play in the middle of the park.
His partnership with Cafu at defensive midfield is starting to add more shape and quality in the middle of the park which is something Forest have been seriously lacking.