Wes Thomas should have opened the scoring for the home side midway through the first half when he blazed a header over from Simon Francis' cross.
Smith produced a stunning fingertip save to keep out Norwich loanee Andrew Surman's 20-yard curler on the stroke of half-time.
At the other end Tom Craddock had Bournemouth goalkeeper Ryan Allsop scrambling across his line after 18 minutes with a long-range shot which fizzed narrowly wide.
Surman almost doubled the Cherries' lead in the 65th minute when he fired wide from a Ryan Fraser cross while Smith was at his best again 14 minutes from time to turn another fierce Surman drive wide of the post.
- Sports & Recreation
- Andrew Surman
- Ryan Fraser